Rising infection rates were clearly the major driver of the move to continue remote learning. But Mr. Trump’s aggressive, often bellicose demands for reopening classrooms helped to harden the views of many educators that it would be unsafe — and give their powerful unions fodder to demand stronger safety measures or to resist efforts to physically reopen.

“If you had told me that Trump was doing this as a favor to the schools-must-not-open crowd, I’d believe you,” said Rick Hess, the director of education policy at the American Enterprise Institute, a conservative think tank.

Indeed, as the president has pushed for schools to reopen, key constituencies — parents and educators — have largely moved in the other direction.

A July poll by Education Week found that roughly 60 percent of educators said the pandemic had worsened their view of Mr. Trump, who already fared poorly with much of that group. A recent Washington Post poll found that parents disapprove of Mr. Trump’s handling of school reopening by a two-thirds majority. And a new Gallup poll showed that fewer parents want their children to return to school buildings now than they did in the spring.