Even under normal circumstances, paying for child care can be a struggle. Day care for a single child can easily cost $10,000 a year—about the average price of tuition and fees for a year at a public, in-state university—and more in big cities. The cost of child care and nursery school has risen at roughly twice the pace of inflation since 2000, according to the federal Consumer Price Index.

As the pandemic drags on, more parents are in the market for child-care services. School-age children now need sitters during the day. Many day cares have closed. Grandparents can’t fly in.

Kara Fastuca, a special-education teacher in New York City, was expecting her daughter to attend free prekindergarten in September. But she feels the hybrid learning model the city is offering, with children likely in school one or two days most weeks, is inadequate. So she plans to send her daughter—and her infant son—to a babysitter.

That will nearly double the child-care costs she was expecting to pay this fall. A single mother, Ms. Fastuca will be covering the bills on her public-school salary. She saved as much money as she could over the spring and summer to prepare. “It’s still going to be tight,” she said. “But I have to do what I have to do.”