Few American cities have labor politics as fraught as Chicago’s, where the nation’s third-largest school system shut down this week after the teachers’ union members refused to work in person, arguing that classrooms were unsafe amid the Omicron surge.

But in a number of other places, the tenuous labor peace that has allowed most schools to operate normally this year is in danger of collapsing.

While not yet threatening to walk off the job, unions are back at negotiating tables, pushing in some cases for a return to remote learning. They frequently cite understaffing because of illness, and shortages of rapid tests and medical-grade masks. Some teachers, in a rear-guard action, have staged sick outs.

In Milwaukee, schools are remote until Jan. 18, because of staffing issues. But the teachers’ union president, Amy Mizialko, doubts that the situation will significantly improve and worries that the school board will resist extending online classes.

“I anticipate it’ll be a fight,” Ms. Mizialko said.

She credited the district for at least delaying in-person schooling to start the year but criticized Democratic officials for placing unrealistic pressure on teachers and schools.

“I think that Joe Biden and Miguel Cardona and the newly elected mayor of New York City and Lori Lightfoot — they can all declare that schools will be open,” Ms. Mizialko added, referring to the U.S. education secretary and the mayor of Chicago. “But unless they have hundreds of thousands of people to step in for educators who are sick in this uncontrolled surge, they won’t be.”

For many parents and teachers, the pandemic has become a slog of anxiety over the risk of infection, child care crises, the tedium of school-through-a-screen and, most of all, chronic instability.

And for Democrats, the revival of tensions over remote schooling is a distinctly unwelcome development.

Because they have close ties to the unions, Democrats are concerned that additional closures like those in Chicago could lead to a possible replay of the party’s recent loss in Virginia’s governor race. Polling showed that school disruptions were an important issue for swing voters who broke Republican — particularly suburban white women.

“It’s a big deal in most state polling we do,” said Brian Stryker, a partner at the polling firm ALG Research whose work in Virginia indicated that school closures hurt Democrats.

“Anyone who thinks this is a political problem that stops at the Chicago city line is kidding themselves,” added Mr. Stryker, whose firm polled for President Biden’s 2020 campaign. “This is going to resonate all across Illinois, across the country.”

More than one million of the country’s 50 million public school students were affected by districtwide shutdowns in the first week of January, many of which were announced abruptly and triggered a wave of frustration among parents.

“The kids are not the ones that are seriously ill by and large, but we know kids are the ones suffering from remote learning,” said Dan Kirk, whose son attends Walter Payton College Preparatory High School in Chicago, which was closed amid the district’s standoff this week.

Several nonunion charter-school networks and districts temporarily transitioned to remote learning after the holidays. But as has been true throughout the pandemic, most of the temporary districtwide closures — including Detroit, Cleveland, Milwaukee — are taking place in liberal-leaning areas with powerful unions and a more cautious approach to the coronavirus.

The unions’ demands echo the ones they have made for nearly two years, despite all that has changed. There are now vaccines and the reassuring knowledge that in-school transmission of the virus has been limited. The Omicron variant, while highly contagious, appears to cause less severe illness than previous iterations of Covid-19.

Most district leaders and many educators say it is imperative for schools to remain open. They cite a large body of research showing that closures harm children, academically and emotionally, and widen income and racial disparities.

But some local union officials are far warier of packed classrooms. In Newark, schools began 2022 with an unexpected stretch of remote learning, set to end on Jan. 18. John Abeigon, the Newark Teachers Union president, said he was hopeful about the return to buildings but that he remained unsure if every school could operate safely. Student vaccination is far from universal, and most parents have not consented to their children taking regular virus tests.

Mr. Abeigon said that if tests remain scarce, he might ask for remote learning at specific schools with low vaccination rates and high case counts. He agreed that online learning was a burden to working parents but argued that educators should not be sacrificed for the good of the economy.

“I’d see the entire city of Newark unemployed before I allowed one single teacher’s aide to die needlessly,” he said.

In Los Angeles, the district has worked closely with the union to keep classrooms open after one of the longest pandemic shutdowns in the country last school year. The vaccination rate for students 12 and older is about 90 percent, with a student vaccine mandate set to kick in this fall. All students and staff are tested for the virus weekly.

Still, the president of the local union, Cecily Myart-Cruz, would not rule out pushing for a districtwide return to remote learning in the coming weeks. “You know, I want to be honest — I don’t know,” she said.

The tensions are not limited to liberal states. In Kentucky, teachers’ unions and at least one large school district have said they need the flexibility to go remote amid escalating infection rates.

But the Republican-controlled state legislature has granted no more than 10 days for such instruction districtwide, and unions there worry that may be inadequate. Jeni Ward Bolander, a leader of a statewide union, said that teachers may have to walk off the job.

“Frustration is building on teachers,” Ms. Ward Bolander said. “I hate to say we’d walk out at that point, but it’s absolutely possible.”

National teachers’ unions continue to call for classrooms to remain open, but local affiliates hold the most power in negotiations over whether individual districts will close schools.

And over the last decade, some locals, including those in Los Angeles and Chicago, were taken over by activist leaders whose tactics can be more aggressive than those of national leaders like Randi Weingarten of the American Federation of Teachers and Becky Pringle of the National Education Association, both close allies of President Biden.

Complicating matters, some local unions face internal pressure from their own members. In the Bay Area, splinter groups of teachers in both Oakland and San Francisco have planned sick outs, and demanded N95 masks, more virus testing and other safety measures.

Rori Abernethy, a middle-school teacher in San Francisco, organized a sick out there on Thursday. She said the Chicago action had prompted some teachers to ask, “Why isn’t our union doing this?”

In Chicago and San Francisco, working-class parents of color disproportionately send their children to the public schools, and they have often supported strict safety measures during the pandemic, including periods of remote learning. And in New York, the nation’s largest school district, schools are operating in person with increased virus testing, with limited dissent from teachers.

But the politics become more complicated in suburbs, where union leaders may find themselves at odds with public officials at pains to preserve in-person schooling.

In Fairfax County, Virginia’s largest district, the superintendent has a plan for switching individual schools to remote learning in the event of many absent teachers.

Kimberly Adams, the president of the local education association, said her union may want stricter measures. And she said that districts should be planning for virus surges by distributing devices for potential short bursts of online schooling.

But Dan Helmer, a Democratic state delegate whose swing district includes part of Fairfax County, said there was little support among his constituents for a return to online education.

Deb Andraca, a Democratic state representative in Wisconsin whose district lies just north of Milwaukee, where schools went remote this past week, said that Republicans have targeted her seat and that she expected schools to be a line of attack.

“Everyone I know wants schools to stay open,” she said. “But there’s a lot of talk about how teachers’ unions don’t want schools to stay open.”

Jim Hobart, a partner at Public Opinion Strategies, a polling firm that counts several Republican senators and governors as clients, said the school closure issue created two advantages for G.O.P. candidates. It has helped narrow their margins among a demographic they’ve traditionally struggled with — white women between their mid-20s and mid-50s — and it has generally undermined Democrats’ claims to competence.

“A lot of people — Biden, Mayor Lightfoot in Chicago — have said schools should be open,” Mr. Hobart said. “If they’re not able to prevent schools from choosing to close, that shows a weakness on their part.”

Labor officials say that many of their critics are acting in bad faith, exploiting parents’ pandemic-related frustrations to advance longstanding political goals, like discrediting unions and expanding private-school vouchers.

Thus far, neither the critiques nor the broader pandemic challenges appear to have significantly hampered unions’ public standing, even according to polls conducted by researchers skeptical of teachers’ unions.

And if it turns out that Democratic candidates pay a political price for unions’ assertiveness, local labor officials do not consider it to be among their top concerns.

If periods of remote learning this winter hurt the Democratic Party, “that’s a question for the consultants and the brain trusts to figure out,” said Mr. Abeigon, the Newark union president. “But that it’s the right thing to do? There’s no question in my mind.”

Holly Secon contributed reporting from San Francisco.