Districts are also feeling the economic impact of the pandemic, anticipating huge budget shortfalls. And teachers are eager to return to the classroom, saying they miss the energy of real-world interaction with students.

Then there are the educational concerns. To make up for lost classroom time, schools may need to provide remedial instruction, additional special-education services and counseling, said Robin Lake, director of the Center on Reinventing Public Education.

Policy experts are also debating whether students who lag behind in key skills should be held back a grade, or advanced with extra catch-up support.

Mayor Bill de Blasio of New York City, who announced this month that the city’s 1.1 million students would not return to classrooms until September, has said that many children will have to make up for months of lost learning despite the city’s shift to remote instruction.

But there is also a pervasive fear about what it would mean to bring students and teachers back together too quickly, given all that is unknown about how the virus spreads. Forcing educators to work at a perceived risk to their own health could be not only a public health danger but also a recipe for labor unrest in a heavily unionized sector.

Janet Robinson, superintendent of Stratford Public Schools in Connecticut, said she was “horrified” to hear the president urging schools to open. Students in her district were among the first children in the state to test positive. Her staff, including teachers who are cancer survivors, are worried about being rushed back into the classroom.

“I saw the president say, the kids don’t get sick,” Ms. Robinson said. “Well, they’re not in there all by themselves. And I’d hate for a little kid to come into the building, get the virus, and take it home. Then we’d start this thing all over again.”