The Omicron surge threatens to upend any sense of peace in the nation’s education system.

After a holiday break that saw Covid-19 cases spike unrelentingly, a small but growing list of districts — including Newark, Atlanta, Milwaukee and Cleveland — moved temporarily to remote learning for more than 450,000 children.

Districtwide closures, even those that last for a week or two, are a step backward after months in which classrooms largely remained open, even during a fall surge of the Delta variant.

And although politicians, including Mayor Eric Adams of New York and Gov. Ron DeSantis of Florida, vowed to keep schools open, there were growing fears from parents and educators that more districts would soon turn to remote learning — even though in-school transmission of Covid-19 has been limited.

Those decisions could, in turn, radiate through the country, affecting child care, employment and any confidence that the pandemic’s viselike grip was loosening.

announced on Saturday that classes would be online for the first week of January, just days after saying that classes would be held in person.

widened during previous phases of the pandemic.

“There is a casualness with which some have approached closing schools that I find deeply concerning, precisely because of the severe harms we’ve seen accumulate over the past year when schools were closed,” said Joseph Allen, a Harvard University professor who studies indoor environmental quality, including in schools.

the Chicago Teachers Union are preparing to vote on Tuesday on whether to refuse to report to schools starting the following day. The union, which has repeatedly clashed with Mayor Lori Lightfoot’s administration, had demanded that every student be tested for the virus before returning from winter break, a step the district did not take.

The district, one of the largest in the country, instead gave tens of thousands of students optional take-home P.C.R. tests before winter break, which parents were supposed to bring to a FedEx drop box.

On Monday, it became clear that the testing effort had largely failed. Of 35,590 tests recorded by the district in the week ending Saturday, 24,843 had invalid results. Among the minority of tests that did produce results, 18 percent were positive.

A district official said test vendors were looking into the reasons for the inconclusive results.

At a news conference on Monday, the union’s vice president, Stacy Davis Gates, expressed her anger at having “to continuously fight for the basic necessities, the basic mitigations.”

In Florida, Gov. Ron DeSantis reiterated on Monday that officials would not allow the state’s public schools to close, despite a major spike in coronavirus cases.

“You have worse outcomes by closing schools,” said Mr. DeSantis, a Republican who has increased his national profile by rejecting coronavirus lockdowns and mandates for much of the pandemic. “Kids need to be in school.”