Karina Garcia-Jerez, a single mother in the Bronx who worked as a house cleaner and babysitter before the coronavirus outbreak, said she used to complain about her daughters’ teachers on occasion. Since the crisis began, though, she said she has come to rely on them in ways she never anticipated.

Ms. Garcia-Jerez’s younger daughter, Emely, has Down syndrome. The hours when Emely and her sister check in with their teachers and classmates online offer Ms. Garcia-Jerez her only moments of respite from the grind of solo housework and child care.

Teaching is “a really awesome profession,” she said. “It has to come from your soul, like doctors.”

New York City has seen perhaps the most drastic display of unions pushing back against the new expectations placed on teachers.

By the time remote learning started in the nation’s largest school district in late March, many of the city’s roughly 75,000 teachers were already frustrated with New York’s leaders, who waited longer than those in some other major cities to close public schools. Then, Gov. Andrew M. Cuomo announced that spring break, scheduled to begin in early April, would be canceled for schools across the state. (Many other places did the opposite, keeping or even extending their breaks.)

New York City’s teachers’ union, the United Federation of Teachers, held out hope that educators could still take off for Passover and Good Friday — and was furious when Mayor Bill de Blasio kept them on the job for those religious holidays.

“Never once during this crisis has the mayor thanked you for your service,” the union’s president, Michael Mulgrew, wrote in a scathing email to his members. “Instead, he diminishes your work by describing it only as a vehicle to keep children at home.”

Union officials said they were fighting to make sure New York’s teachers were not forced to work more in a day than the six hours and 20 minutes in their contracts. A politically progressive caucus within the union is calling on its leaders to push for “less academic work” during the coming months, and to lobby for a moratorium on student grades and teacher evaluations.