The teachers’ union president, Michael Mulgrew, has said he does not believe schools can reopen at all if the city does not receive additional federal funding this summer.

With many teachers reluctant to return to work, according to polls, staffing will be a major challenge for districts across the country. New York estimates that about 1 in 5 of its teachers will receive a medical exemption to teach remotely this fall.

Matthew Landau, a history teacher at Democracy Prep Charter High School in Harlem, hopes he will be one of them. He survived stage four cancer several years ago and said he does not feel comfortable going back to his classroom.

“I feel there’s no way to keep immunocompromised teachers safe,” he said.

Kevin Kearns, a high school English teacher at the High School of Fashion Industries in downtown Manhattan, has spent the last few weeks wrestling with his own dilemma.

Mr. Kearns and his wife became parents in March, and need child care for their infant son. Their only option is to have Mr. Kearns’ mother-in-law, who is in her 70s, stay with them. Mr. Kearns is terrified of bringing the virus home.

“I don’t want to go back, I don’t think it’s safe to go back, but I don’t know that I necessarily have a choice,” he said.

Still, Mr. Kearns said he feels a duty to the mostly low-income, Black and Latino students he teaches.

“It puts me in a very difficult moral conundrum,” he said, “to choose between supporting my community, students, colleagues and my own family’s safety.”

Erica L. Green contributed reporting.