loss of purchasing power over time, meaning your dollar will not go as far tomorrow as it did today. It is typically expressed as the annual change in prices for everyday goods and services such as food, furniture, apparel, transportation costs and toys.

Americans found themselves with a lot of money in the bank, and as they spent that money on goods, demand collided with a global supply chain that was too fragile to catch up.

Virus outbreaks shut down factories, ports faced backlogs and a dearth of truckers roiled transit routes. Americans still managed to buy more goods than ever before in 2021, and foreign factories sent a record sum of products to U.S. shops and doorsteps. But all that shopping wasn’t enough to satisfy consumer demand.

stop spending at the start of the pandemic helped to swell savings stockpiles.

And the Federal Reserve’s interest rates are at rock bottom, which has bolstered demand for big purchases made on credit, from houses and cars to business investments like machinery and computers. Families have been taking on more housing and auto debt, data from the Federal Reserve Bank of New York shows, helping to pump up those sectors.

But if stimulus-driven demand is fueling inflation, the diagnosis could come with a silver lining. It may be easier to temper consumer spending than to rapidly reorient tangled supply lines.

People may naturally begin to buy less as government help fades. Spending could shift away from goods and back toward services if the pandemic abates. And the Fed’s policies work on demand — not supply.

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Biden Says Spending Bill Will Slow Inflation. But When?

Rocketing inflation has become a headache for U.S. consumers, and President Biden has a go-to prescription. He says a key way to help relieve increasing prices is to pass a $1.85 trillion collection of spending programs and tax cuts that is currently languishing in the Senate.

A wide range of economists agree with the president — but only in part. They generally accept his argument that in the long run, the bill and his infrastructure plan could make businesses and their workers more productive, which would help to ease inflation as more goods and services are produced across the economy.

But many researchers, including a forecasting firm that Mr. Biden often cites to support the economic benefits of his proposals, say the bill is structured in a way that could add to inflation next year, before prices have had time to cool off.

Some economists and lawmakers worry about the timing, arguing that the risk of fueling more inflation when it has reached record highs outweighs the potential benefits of passing a big spending bill that could help to keep prices in check while addressing other social goals. Prices have picked up by 6.2 percent over the past year, the fastest pace in 31 years and far above the Federal Reserve’s inflation target.

Joe Manchin III of West Virginia, has questioned whether high and rising prices should persuade lawmakers to tone down their ambitions.

“West Virginians are concerned about rising inflation,” he said on Twitter last week. “We cannot throw caution to the wind & continue to pile on debt that our country can’t afford.”

Democrats preparing to push it to a House vote as early as next week. But timing is uncertain in the Senate, where a vote is likely to be changed or delayed in response to Mr. Manchin’s concerns.

The extent to which Mr. Biden’s $1.85 trillion bill exacerbates inflation largely depends on how much it stimulates the economy and whether Americans increase their spending as a result of the legislation — and when all of that occurs.

Many economists say it could create a short-term stimulus because the plan is structured to raise money gradually by taxing wealthier Americans, who are less likely to spend each additional dollar they have, and redistribute it quickly to people who earn less and are more likely to spend newfound cash.

Because of the difference in timing between when the government spends money and when it starts to bring in more revenue, the bill is expected to pump money into the economy in its early years. Moody’s Analytics — the firm that the White House typically cites when arguing in favor of its legislation — estimates that the government will spend $163 billion more on the package than it takes in next year. And the redistribution could make the money more potent as economic stimulus.

“The spending is designed to go to the people who are more likely to spend it than to save it,” said Ben Ritz, the director of the Progressive Policy Institute’s Center for Funding America’s Future. But more than any specific program, “the bigger inflationary issue is the math.”

White House economists have countered those arguments. If the bill passes, they say, it would do relatively little to spur increased consumer spending next year and not nearly enough to fully offset the loss of government stimulus to the economy as pandemic aid expires. That the program spends more heavily next year is a feature, they say, because it will partly blunt the economic drag as fiscal help fades. They note that the bill is intended to be offset completely by tax increases and other revenue savings.

And they argue that by increasing the economy’s capacity to churn out goods and services, the president’s infrastructure plan and his broader program could both help to moderate costs over time.

Mr. Summers has argued.

There is less economic or political debate about Mr. Biden’s $1 trillion infrastructure plan, which cleared Congress last week and which the president will sign on Monday. Economists — including conservative ones — largely agree that it is likely to eventually expand the capacity of the economy, and that it is small and spread out enough that it will not meaningfully fuel faster inflation in the near term.

Among Democrats, there is widespread support for the economic ambitions contained in the administration’s broader spending bill, which aims to create more equity for low- and middle-class earners and a bigger safety net for working parents. But the measure is drawing more complicated reviews when it comes to its immediate effect on inflation.

Economists at Moody’s found in a recent analysis that the administration’s full agenda would slightly increase inflation in 2022, though they did not expect the program to ultimately raise it because of benefits that would later ease supply constraints. It estimates that with the infrastructure bill alone, inflation will be running at a 2.1 percent annual rate by the final quarter of next year. If the larger spending bill also passes, that grows to 2.5 percent.

But Moody’s baseline assumption that inflation will moderate by the end of next year is relatively optimistic. Bank of America’s economics team said that core consumer prices would still rise at a 3.2 percent rate at the end of next year, incorporating the assumption that Mr. Biden’s plan passes.

companies scramble for workers, prices rise and supply chains struggle to keep pace with booming demand, this is the wrong moment to hit the economy with any added juice.

“We don’t have a lot of spare capacity,” said Kristin J. Forbes, an economist at the Massachusetts Institute of Technology. “We certainly don’t have a lot of spare workers today.”

Inflation looms more significantly in the near term because it is currently high, and if it remains that way for an extended period, consumers could change their behaviors and expectations, locking in faster gains. People who worry about the proposals say that 2022 is the wrong time to hand households more money.

Maya MacGuineas, the president of the Committee for a Responsible Federal Budget, said she was unsure whether the package would fuel inflation. But given the current pace of price increases, “you have to be more careful than you would be otherwise.”

The White House says the provisions of the bill that put money in families’ pockets, such as child care help, are not simple stimulus. They will allow caregivers into the labor market, they argue, an investment in the economy’s future that will allow it to produce more with time.

That makes the new program different from the spending passed earlier this year. The Biden administration increasingly acknowledges that sending households checks and offering expanded unemployment insurance supplemented savings, and that as households had more wherewithal to spend it helped to drive up prices.

Mr. Biden said in Baltimore on Wednesday. But the White House contends that this program is not the same as the previous package, and that it will make the price situation better, not worse.

“According to the economic experts, this bill is going to ease inflationary pressures,” the president said on Wednesday.

Still, the 17 Nobel Prize-winning economists that the White House regularly cites have specified that capacity improvements will ease inflation over time rather than imminently.

“Because this agenda invests in long-term economic capacity and will enhance the ability of more Americans to participate productively in the economy,” they wrote, “it will ease longer-term inflationary pressures.”

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Once a Leading Polluter, the U.K. Is Now Trying to Lead on Climate Change

LONDON — As Britain prepares to host a landmark climate summit in Glasgow this week, the milestones of its own evolution to a more climate-friendly economy are on vivid display along the railroad line from London to Scotland.

Near Gainsborough, a river town 150 miles north of the capital, one of Britain’s last coal-fired power plants still spews carbon dioxide and other gases into the air. Another 150 miles north, off the coast of the seaside port of Blyth, the slender blades of five turbines in an offshore wind farm turn lazily in the breeze.

The two plants, both owned by the French utility giant EDF, illustrate how far Britain has come. The coal station, restarted recently to cover a shortfall in electricity, is slated to be taken out of operation next year, while the company plans to install experimental floating turbines in the waters off Blyth.

“We’re talking about a huge transition,” said Paul Spence, the director of strategy and corporate affairs at EDF, referring to Britain’s goal of being a carbon-neutral economy by 2050. “A lot of things need to happen to keep the lights on.”

climate meeting, known as COP26, it has a credible claim to being a global leader in climate policy. The birthplace of the Industrial Revolution, Britain became the first country to legally mandate reductions in greenhouse-gas emissions through the Climate Change Act in 2008. Its high-tech windmills and superannuated smokestacks are only the most visible evidence of a three-decade campaign.

Having built the world’s largest offshore wind industry, Britain has reduced emissions by 44 percent from 1990 levels. Its target to cut them by at least 68 percent by 2030 is one of the most ambitious of any major economy, according to the Climate Action Tracker, a scientific analysis of the policies of countries.

If Britain achieves that target, which is far from clear, it would be one of a handful of countries doing enough to fulfill the key goal of the Paris Agreement: limiting the long-term rise in the planet’s temperatures to 1.5 degrees Celsius.

showdown with striking coal miners in 1984. By crushing the union and slashing subsidies for the coal industry, Mrs. Thatcher accelerated Britain’s search for alternative energy sources, namely natural gas.

“She got rid of the coal miners for a combination of political and economic reasons,” said Tom Burke, the chairman of E3G, an environmental think tank, and a former government adviser. “But it gave the U.K. a degree of freedom of action that wasn’t available to other countries.”

she said to the United Nations.

Mrs. Thatcher planted the seed for a bipartisan cause, as Conservative and Labour governments sought to burnish their green credentials. British diplomats played key roles in brokering climate deals in Rio de Janeiro and Kyoto, Japan. Britain installed climate attachés in its embassies around the world.

In 2006, a British government adviser, Nicholas Stern, produced a seminal study of the economic effects of climate change, which framed the debate before the 2009 summit in Copenhagen and set the stage for the Climate Act, passed under a Labour prime minister, Gordon Brown.

When the Conservatives came to power in 2010, they viewed climate policy as a way to appeal to younger voters, many of whom viewed the Tories as a tightfisted party in thrall to business interests. Parliament created a climate change committee, which prodded the government to adopt policies that would help Britain meet its goals. Several of its policies were mimicked by fellow European Union members. “We basically ran the E.U. on climate policy,” Mr. Burke said.

Then came the Brexit vote in 2016, and “we lost our most important tool for influencing other countries, which was the E.U,” he said.

Mr. Johnson, who once scoffed that wind farms would “barely pull the skin off a rice pudding,” now speaks about climate change with the zeal of the converted. Allies say he has been convinced of the need for action by his third wife, Carrie Johnson, who campaigns against plastic pollution.

But critics say Mr. Johnson’s bracing words are belied by his actions. The Climate Action Tracker, while praising Britain’s ambitions, criticized its financial commitment to achieving them, calling it “highly insufficient.”

“It’s accurate to say that this is a betrayal of a national commitment by the current government,” Mr. Burke said.

Mr. Johnson’s pro-Brexit government, he said, depends on support from the libertarian wing of the Tory party, which opposes far-reaching climate initiatives, while his anti-business messaging hinders partnerships with the private sector.

For private companies, the government’s messaging has been muddled. EDF said it would like to build more onshore wind farms, but local resistance and lack of incentives has made it less attractive. And the government has struggled to line up financing for a new generation of nuclear plants.

“We’re only a quarter of the way toward the decarbonized energy system that the prime minister set as a goal for 2035,” said Mr. Spence, of EDF. “We need all the answers, faster than we’ve ever done them before, if we’re going to get anywhere close to a 1.5-degree world.”

For all of Britain’s agenda-setting, there is also a sense among activists and experts that there is only so much a midsize country can do to solve a planetary problem. Its total emissions account for barely 1 percent of the world’s total. China accounts for nearly 30 percent, and the United States for 14 percent.

“Imagine if these policies had been picked up in 1997 by the United States,” said David King, a former climate envoy and scientific adviser to Prime Minister Tony Blair. “The world would be a very different place.”

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Persistent Inflation Threatens Biden’s Agenda

WASHINGTON — At least once a week, a team of President Biden’s top advisers meet on Zoom to address the nation’s supply chain crisis. They discuss ways to relieve backlogs at America’s ports, ramp up semiconductor production for struggling automakers and swell the ranks of truck drivers.

The conversations are aimed at one goal: taming accelerating price increases that are hurting the economic recovery, unsettling American consumers and denting Mr. Biden’s popularity.

An inflation surge is presenting a fresh challenge for Mr. Biden, who for months insisted that rising prices were a temporary hangover from the pandemic recession and would quickly recede. Instead, the president and his aides are now bracing for high inflation to persist into next year, with Americans continuing to see faster — and sustained — increases in prices for food, gasoline and other consumer goods than at any point this century.

That reality has complicated Mr. Biden’s push for sweeping legislation to boost workers, expand access to education and fight poverty and climate change. And it is dragging on the president’s approval ratings, which could threaten Democrats’ already tenuous hold on Congress in the 2022 midterm elections.

CNBC and Fox News show a sharp decline in voter ratings of Mr. Biden’s overall performance and his handling of the economy, even though unemployment has fallen quickly on his watch and economic output has strengthened to its fastest rate since Ronald Reagan was president. Voter worry over price increases has jumped in the last month.

via executive actions.

“There are distinct challenges from turning the economy back on after the pandemic that we are bringing together state and local officials, the private sector and labor to address — so that prices decrease,” Kate Berner, the White House deputy communications director, said in an interview.

Mr. Biden’s top officials stress that the administration’s policies have helped accelerate America’s economic rebound. Workers are commanding their largest wage gains in two decades. Growth roared back in the first half of the year, fueled by the $1.9 trillion economic aid bill the president signed in March. America’s expansion continues to outpace other wealthy nations around the world.

Inflation has risen in wealthy nations across the globe, as the pandemic has hobbled the movement of goods and component parts between countries. Virus-wary consumers have shifted their spending toward goods rather than services, travel and tourism remain depressed, and energy prices have risen as demand for fuel and electricity has surged amid the resumption of business activity and some weather shocks linked to climate change.

But some economists, including veterans of previous Democratic administrations, say much of Mr. Biden’s inflation struggle is self-inflicted. Lawrence H. Summers is one of those who say the stimulus bill the president signed in March gave too much of a boost to consumer spending, at a time when the supply-chain disruptions have made it hard for Americans to get their hands on the things they want to buy. Mr. Summers, who served in the Obama and Clinton administrations, says inflation now risks spiraling out of control and other Democratic economists agree there are risks.

“The original sin was an oversized American Rescue Plan. It contributed to both higher output but also higher prices,” said Jason Furman, a Harvard economist who chaired the White House Council of Economic Advisers under President Barack Obama.

That has some important Democrats worried about price-related drawbacks from the president’s ambitious spending package, complicating Mr. Biden’s approach.

ease the pain of high-profile price spikes, like gasoline. Some in his administration have pushed for mobilizing the National Guard to help unclog ports that are stacked with imports waiting to be delivered to consumers around the country. Mr. Biden has raised the possibility of tapping the strategic petroleum reserve to modestly boost oil supplies, or of negotiating with oil producers in the Middle East to ramp up.

During a CNN town hall last week, Mr. Biden conceded the limits of his power, saying, “I don’t have a near-term answer” for bringing down gas prices, which he does not expect to begin dropping until next year.

“I don’t see anything that’s going to happen in the meantime that’s going to significantly reduce gas prices,” he said.

Janet L. Yellen, the Treasury secretary, told CNN’s “State of the Union” on Sunday that she expects improvement in the overall inflation rate “by the middle to end of next year, second half of next year.”

With an American public that had gone nearly 40 years without seeing — or worrying — about inflation, the issue provides an opening for the opposition. Republicans have turned price spikes into a weapon against Mr. Biden’s economic policies, warning that more spending would exacerbate the pain for everyday Americans.

“It’s everywhere,” said Representative Kevin Brady of Texas, the top Republican on the Ways and Means Committee, in an interview. “You can’t live your life without seeing your paycheck buy less.”

White House officials have monitored inflationary pressure for months. They remain convinced, as they were in April, that price increases will not spiral out of control and force abrupt interest-rate increases from the Federal Reserve that could slam the brakes on growth.

The president and his top advisers remain confident that price growth will start to fall well before the midterms. They defend the size of the rescue plan and say Americans are focused on inflation right now because the success of the stimulus bill accelerated economic and employment growth and took a larger issue — the availability of jobs for people who want them — off the table.

“It is a highly incomplete view to try to assess the economy, and even people’s views about the economy, by looking at inflation alone,” Jared Bernstein, a member of Mr. Biden’s Council of Economic Advisers, said in an interview. “You also have to appreciate the robustness of the expansion, and how it’s lifting job and earnings opportunities.”

Mr. Bernstein and other advisers say many of the causes of inflation are already improving. They point to calculations by Mark Zandi, a Moody’s Analytics economist, that suggest Americans who have left the labor force will begin flocking back into the job market by December or January, because they will likely have exhausted their savings by then.

The advisers are also continuing to explore more actions they could take, including efforts to increase the number of truck drivers near ports and to force lower prices and more competition in the food industry.

“We are always all in on everything,” Ms. Berner said.

To which many officials add a caveat: Almost anything the White House could do now will take time to push prices down.

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How Chemours and DuPont Avoid Paying for PFAS Pollution

The transactions that created Chemours and reinvented DuPont laid the groundwork for a blame-shifting exercise that has made it difficult for regulators and others to hold anyone accountable for decades of contamination in North Carolina and elsewhere.

State attorneys general in Ohio, New Jersey, New Hampshire, Vermont and New York each sued the companies for having released toxic chemicals into the air, water and soil and for concocting a spinoff to shield DuPont from responsibility. Dutch prosecutors began criminally investigating Chemours for the use of PFOA at a factory in Dordrecht from 2008 to 2012, before Chemours was created.

Yet in courts, in the media and in public settings, DuPont and Chemours have used the spinoff to distance themselves from the problems.

In a court filing in Ohio, where the state has sued over pollution from the Washington Works factory on the West Virginia border, Chemours claimed that the contamination happened before “Chemours even came into existence.” In a securities filing this summer, Chemours stated that it “does not, and has never, used” PFOA. Yet Chemours continues to manufacture other versions of PFAS, including GenX.

DuPont adopted a similar stance. Because Chemours was independent and had assumed responsibility for Washington Works, DuPont claimed it had nothing to do with the pollution. In fact, DuPont insisted, because it was technically a new company, it had never even made the toxic substances in question.

In 2019, Chemours, deep in debt, sued DuPont. Chemours contended that the spinoff was conceived to get DuPont off the hook for its decades of pollution. According to the complaint, DuPont executives decided against a $60 million project that would have stopped Fayetteville Works from discharging chemicals into the Cape Fear River. Instead, DuPont executives made a $2 million change, which they abandoned shortly before they announced the Chemours spinoff.

The lawsuit asked, “Why bother spending money to fix the problem, DuPont apparently reasoned, when it could be conveniently passed on to Chemours?”

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A Fading Coal County Bets on Schools, but There’s One Big Hitch

“I hear it from kids all the time: I want to get out of here,” said Kristin Johnson, a 24-year-old middle school teacher at Mount View who lives in Princeton, W.Va., about an hour’s drive away, and is itching for a teacher job to open there. “Those who do get an education know they can make more money somewhere else.”

Ms. Keys returned, in part, out of loyalty. “When I was in high school, we started losing a lot of teachers,” she said. “People feared there would be nobody there to take those jobs.” But a stable teaching job, as well as free housing at her grandmother’s old house, played into her calculations.

This may not be enough to hold her, though. Even dating locally is complicated. Her boyfriend lives over an hour away, outside Beckley. “There is nobody here that is appealing,” Ms. Keys said.

Consider Emily Hicks, 24, who graduated from Mount View in 2015. She is at the forefront of Reconnecting McDowell’s efforts, an early participant in the mentoring program meant to expand the horizons of local youths.

She didn’t even have to leave home to get her bachelor’s degree at Bluefield State College, commuting from home every other day. Today she teaches fifth grade at Kimball Elementary School. Her father is a surveyor for the coal mines; her mother works for the local landfill. But her boyfriend, Brandon McCoy, is hoping to leave the coal business and has taken a couple of part-time jobs at clinics outside the county after getting an associate degree in radiology.

Her brother, Justin, who graduated from high school in June, is going to college to get a degree in electrical engineering. “I have no idea what I’m going to do after that,” he said. “But there’s not a lot to do here.”

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Paul J. Hanly Jr., Top Litigator in Opioid Cases, Dies at 70

Paul J. Hanly Jr., a top trial lawyer who had been central to the current nationwide litigation against pharmaceutical companies and others in the supply chain for their role in the deadly opioid epidemic, died on Saturday at his home in Miami Beach. He was 70.

The cause was anaplastic thyroid cancer, an extremely rare and aggressive disease, said Jayne Conroy, his longtime law partner.

Over his four-decade career, Mr. Hanly, a class-action plaintiffs’ lawyer, litigated and managed numerous complex legal cases, involving among other things the funding of terrorists, stemming from the attacks of Sept. 11, 2001, and allegations of the sexual abuse of dozens of boys by a man who ran an orphanage and school in Haiti.

But nothing compares to the national opioid cases that are pending in federal court in Cleveland on behalf of thousands of municipalities and tribes against the manufacturers and distributors of prescription opioid pain medications. The federal opioid litigation is regarded by many as perhaps the most complex in American legal history — even more entangled and far-reaching than the epic legal battles with the tobacco industry.

settled with Purdue for $75 million. It was one of the few instances in which a drug maker agreed to pay individual patients who had accused it of soft-pedaling the risk of addiction.

Mr. Hanly had a history of taking on complex cases with vast numbers of plaintiffs. Shortly after the 2001 terrorist attacks, he represented some of the families who had lost loved ones on the planes and in the World Trade Center. He also filed suit to stop the sale of tanzanite, a raw stone used as a cash alternative to fund terrorist activities. That lawsuit was expanded to include foreign governments, banks and others that supported Al Qaeda. Portions of it remain pending.

Another of his important cases was a 2013 landmark settlement of $12 million on behalf of 24 Haitian boys who said they had been sexually abused by Douglas Perlitz, who ran programs for underprivileged boys and was subsequently sentenced to 19 years in prison. Mr. Hanly said the defendants, including the Society of Jesus of New England, Fairfield University and others, had not properly supervised Mr. Perliitz. Mr. Hanly filed additional charges in 2015, bringing the total number of abused youths to more than 100 between the late 1990s and 2010.

“Paul was a lawyer’s lawyer,” said Ms. Conroy, his law partner. She said he was renowned for his exhaustive trial preparation, his creative trial strategies and his nearly photographic memory of the contents of documents.

He was also known for veering sartorially from the muted grays and blacks of most lawyers to more jaunty attire in bright yellows, blues and pinks. He favored bespoke styles that were flashy yet sophisticated. His two-tone shoes were all handmade.

John V. Kenny, a former mayor of Jersey City and a powerful Hudson County Democratic boss known as “the pope of Jersey City,” who was jailed in the 1970s after pleading guilty to charges of income tax evasion.

Mr. Hanly took a different path. He went to Cornell, where his roommate was Ed Marinaro, who went on to play professional football and later became an actor (best known for “Hill Street Blues”). Mr. Hanly, who played football with him, graduated in 1972 with a major in philosophy and received a scholar-athlete award as the Cornell varsity football senior who combined the highest academic average with outstanding ability.

He earned a master’s degree in philosophy from Cambridge University in 1976 and a law degree from Georgetown in 1979. He then clerked for Lawrence A. Whipple, a U.S. District Court judge in New Jersey.

Mr. Hanly’s marriage in the mid-1980s to Joyce Roquemore ended in divorce. He is survived by two sons, Paul J. Hanly III and Burton J. Hanly; a daughter, Edith D. Hanly; a brother, John K. Hanly; and a sister, Margo Mullady.

He began his legal career as a national trial counsel and settlement counsel to Turner & Newall, a British asbestos company, one of the world’s largest, in its product-liability cases. The company was purchased by an American firm, Federal-Mogul, in 1998, after which it was overwhelmed with asbestos claims and filed for bankruptcy in 2001.

Mr. Hanly and Ms. Conroy spent much of their time steeped in negotiations with plaintiffs’ lawyers. They soon switched to representing plaintiffs themselves.

“We recognized over time that that was more important to us,” Ms. Conroy said, “to make sure victims were compensated for what happened.”

Jan Hoffman contributed reporting.

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Republicans Reject Biden’s Bipartisan Infrastructure Deal

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WASHINGTON — The Biden administration sent Senate Republicans an offer on Friday for a bipartisan infrastructure agreement that sliced more than $500 billion off the president’s initial proposal, a move that White House officials hoped would jump-start the talks but that Republicans swiftly rejected.

The lack of progress emboldened liberals in Congress to call anew for Mr. Biden to abandon his hopes of forging a compromise with a Republican conference that has denounced his $4 trillion economic agenda as too expensive and insufficiently targeted. They urged the president instead to begin an attempt to move his plans on a party-line vote through the same process that produced his economic stimulus legislation this year.

Mr. Biden has said repeatedly that he wants to move his infrastructure plans with bipartisan support, which key centrist Democrats in the Senate have also demanded. But the president has insisted that Republicans spend far more than they have indicated they are willing to.

He also says that the bill must contain a wide-ranging definition of “infrastructure” that includes investments in fighting climate change and providing home health care, which Republicans have called overly expansive.

countered with a $568 billion plan, though many Democrats consider that offer even smaller because it includes extensions of some federal infrastructure spending at expected levels. In a memo on Friday to Republicans, obtained by The New York Times, Biden administration officials assessed the Republican offer as no more than $225 billion “above current levels Congress has traditionally funded.”

The president’s new offer makes no effort to resolve the even thornier problem dividing the parties: how to pay for that spending. Mr. Biden wants to raise taxes on corporations, which Republicans oppose. Republicans want to repurpose money from Mr. Biden’s $1.9 trillion economic aid package, signed in March, and to raise user fees like the gas tax, which the president opposes.

Mr. Biden “fundamentally disagrees with the approach of increasing the burden on working people through increased gas taxes and user fees,” administration officials wrote in their memo to Republican negotiators. “As you know, he made a commitment to the American people not to raise taxes on those making less than $400,000 per year, and he intends to honor that commitment.”

Still, the new proposal shows some movement from the White House. It cuts out a major provision of Mr. Biden’s “American Jobs Plan”: hundreds of billions of dollars for advanced manufacturing and research and development efforts meant to position the United States to compete with China for dominance in emerging industries like advanced batteries. Lawmakers have included some, but not all, of the administration’s proposals in those areas in a bipartisan bill currently working its way through the Senate.

Mr. Biden’s counteroffer would also reduce the amount of money he wants to spend on broadband internet and on highways and other road projects. He would essentially accept the Republicans’ offer of $65 billion for broadband, down from $100 billion, and reduce his highway spending plans by $40 billion to meet them partway. And it would create a so-called infrastructure bank, which seeks to use public seed capital to leverage private infrastructure investment — and which Republicans have pushed for.

Republican senators who were presented the offer in a conference call with administration officials on Friday expressed disappointment in it, even as they vowed to continue talks.

“During today’s call, the White House came back with a counteroffer that is well above the range of what can pass Congress with bipartisan support,” said Kelley Moore, a spokeswoman for Senator Shelley Moore Capito of West Virginia, who is leading the Republican negotiating group.

“There continue to be vast differences between the White House and Senate Republicans when it comes to the definition of infrastructure, the magnitude of proposed spending, and how to pay for it,” Ms. Moore said. “Based on today’s meeting, the groups seem further apart after two meetings with White House staff than they were after one meeting with President Biden.”

The updated White House offer drew immediate pushback from progressives as well, illustrating the extent to which the forces pushing against a deal are bipartisan. Senator Edward J. Markey, Democrat of Massachusetts, urged his party not to “waste time” haggling over details with Republicans who do not share their vision for what the country needs.

“A smaller infrastructure package means fewer jobs, less justice, less climate action, and less investment in America’s future,” Mr. Markey said in a news release.

Democratic leaders on Capitol Hill have watched the talks skeptically, wary that Republicans will eat up valuable time on the legislative calendar and ultimately refuse to agree to a deal large enough to satisfy liberals. While they have given the White House and Republican senators latitude to pursue an alternative, party leaders are under increasing pressure from progressives to move a bill unilaterally through the budget reconciliation process in the Senate.

They have quietly taken steps to make that possible in case the talks collapse. Aides to Senators Chuck Schumer, Democrat of New York and the majority leader, and Bernie Sanders, independent of Vermont and the chairman of the Budget Committee, met on Thursday with the Senate parliamentarian to discuss options of proceeding without Republicans under the rules.

Biden administration officials were frustrated that Republicans did not move more toward the president in a new offer they presented this week in negotiations on Capitol Hill. They made clear to Republicans on Friday that they expected to see significant movement in the next counteroffer, and that the timeline for negotiations was growing short, a person familiar with the discussions said.

The administration may soon find itself negotiating with multiple groups of senators. A different, bipartisan group plans to meet on Monday night to discuss spending levels and proposals to pay for them. Members of the group — which includes Mitt Romney of Utah, Susan Collins of Maine, Bill Cassidy of Louisiana and Rob Portman of Ohio, all Republicans, as well as Kyrsten Sinema of Arizona and Joe Manchin III of West Virginia, both Democrats — helped draft a bipartisan coronavirus relief bill in December.

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