“I discussed it with my team, and they say the thing that has more impact than anything Trump would say to the MAGA folks is what the local doctor, what the local preachers, what the local people in the community say,” Mr. Biden said, referring to Mr. Trump’s supporters and campaign slogan “Make America Great Again.” Until everyone is vaccinated, Mr. Biden added, Americans should continue to wear masks.

Widespread opposition to vaccination, if not overcome, could slow the United States from reaching the point where the virus can no longer spread easily, setting back efforts to get the economy humming again and people back to a more normal life. While the problem until now has been access to relatively tight supplies of the vaccine, administration officials expect to soon face the possibility of supply exceeding demand if many Americans remain reluctant.

“The national atmosphere around vaccine uptake matters,” said John Bridgeland, the founder and chief executive of Covid Collaborative, a bipartisan group working closely with the White House on issues of vaccine hesitancy. “Although the ground game is the most important thing, having a tail wind behind us at the national level with every single living President and first lady, regardless of party, saying Americans should get this safe and effective vaccine creates the kind of tail winds we are looking for.”

Annie Karni contributed reporting.