GREENSBORO, N.C. — To understand the problems Democrats hope to solve with their supersized plan to make child care better and more affordable, consider this small Southern city where many parents spend more for care than they do for mortgages, yet teachers get paid like fast food workers and centers cannot hire enough staff.

With its white pillars and soaring steeple, the Friendly Avenue Baptist Church evokes an illusory past when fathers left for work, mothers stayed home to mother, and education began when children turned five. But its sought-after preschool illuminates the dilemmas of modern family life.

Until their elder son started kindergarten this fall, Jessica and Matt Lolley paid almost $2,000 a month for their two boys’ care — roughly a third of their income and far more than their payments on their three-bedroom house. But one of the teachers who watched the boys earns so little — $10 an hour — that she spends half her time working at Starbucks, where the pay is 50 percent higher and includes health insurance.

The center’s director wants to raise wages, but has little room to pass along costs to parents who are already stretched. She has been trying since February to replace a teacher who quit without warning; four applicants accepted the job in turn, but none showed up.

“I’ve been an administrator for 30 years, and I’ve never seen anything like this,” said the director, Sandy Johnson. “Directors are at the point where they’re willing to hire anyone who walks through the door. The children deserve far more than that, and the families deserve far more than that.”

Democrats describe the problem as a fundamental market failure — it simply costs more to provide care than many families can afford — and are pushing an unusually ambitious plan to bridge the gap with federal subsidies.

The huge social policy bill being pushed by President Biden would cap families’ child care expenses at 7 percent of their income, offer large subsidies to child care centers, and require the centers to raise wages in hopes of improving teacher quality. A version before the House would cost $250 billion over a decade and raise annual spending fivefold or more within a few years. An additional $200 billion would provide universal prekindergarten.

“This would be the biggest investment in the history of child care,” said Stephanie Schmit, an analyst at the Center for Law and Social Policy, a research group that supports the measure. “For too long, parents have had to struggle with the high cost of care, while child care providers have been incredibly undervalued and underpaid. This is a once-in-a-generation opportunity to do right for everyone.”

Prospects remain uncertain for the broader bill, which includes new educational, health care, and child-rearing subsidies. Some Democrats balked at Mr. Biden’s request for $3.5 trillion over 10 years and proposed a figure closer to $2 trillion.

Republicans strongly oppose the safety net expansion, saying that it is unaffordable and smacks of socialism, and some conservatives warn the child care provisions would inflate costs, impose burdensome regulations, and penalize parents who prefer informal care.

As Democrats describe it, child care is an issue not just of family finance but of macroeconomics (parents need it to join the work force); brain development (much of which happens before children start school); and racial equity (the low-paid work force is disproportionately composed of minorities).

In Greensboro, parents know little about the Democrats’ plan but much about child care costs, which can cause them to reconfigure work hours, postpone the purchase of cars and appliances, or have fewer children than they desire.

“We had no idea child care was going to cost this much,’’ said Ms. Lolley, who works in human resources for the public school system and whose husband sells plumbing fixtures at Lowe’s. “There’s no way we could afford to have another child.”

Greensboro has been a hub of child care advocacy since at least the early 1990s, when local organizers helped lead a national campaign called Worthy Wages, which sought to raise pay and improve working conditions. The state government is also known as a leader. It offers scholarships to child care workers who want more education and runs two wage-subsidy programs, which together reach about one in eight child care workers and provide average bonuses of roughly $2,400 a year.

Still, the problems of high costs and low wages remain.

“Much of what North Carolina has done is terrific, but it’s going to take the resources of the federal government to make change on the scale we need,” said Rosemarie Vardell, a retired professor who helped lead the Worthy Wages campaign.

The Treasury Department reported last month that the average cost of care is roughly $10,000 a year per child and consumes about 13 percent of family income, nearly twice what the government considers affordable. At the same time, it noted the average teacher earns about $24,000 a year, many live in poverty, and nearly half receive some public assistance.

“It’s among the lowest-paid of all occupations,” said Lea J.E. Austin of the Center for the Study of Child Care Employment. “People have a hard time seeing that this is complex, specialized work.”

The coronavirus pandemic has made the problem worse. Competing employers have raised pay, and some teachers are afraid to supervise children who cannot be vaccinated or masked. Nationally, the work force has declined by about 12 percent from prepandemic levels.

“Everyone I know has significantly increased entry-level pay, and we’re not close to being able to fill positions,” Ms. Johnson, the Friendly Avenue director, said on a recent call with other Greensboro administrators.

“Ditto!” said Donna Danzy, who runs two highly rated centers. “There are dwindling numbers of people interested in doing this kind of work. They are not seeing the joy.”

“There are really great centers who have had to close,” said another director, Devon Walton. “We have a waiting list a mile long.”

While directors say they cannot hire, teachers say they cannot pay their bills. Earning $10 an hour at the Little Leaders Learning Academy, Uvika Joseph, a single mother, got food stamps and Medicaid for her three children. She just left to become an assistant in the public schools, where she expects to earn nearly twice as much and will receive health insurance.

“The only reason I am leaving is the pay,” she said. “I love the kids.”

To make ends meet, Rashelle Myers, who has an associate degree in early childhood education, splits a 60-hour workweek between the Friendly Avenue center and Starbucks. She called the Democrats’ plan to raise wages “amazing” and overdue.

“I make $10 an hour to shape the future of children but make $15 an hour to hand someone a cup of coffee,” she said. “That doesn’t make sense.”

Low pay leads to high turnover, which the Treasury Department said was at least 26 percent a year. April Harden Crocker, a Friendly Avenue teacher, has taught for nearly three decades — “it’s my passion, it’s my heart, I just have to do it” — but she warned that employee churn harms care.

“Babies don’t like strangers’ faces — if you keep bringing new people in, they get really upset,” she said. “If the pay was better we would get more devoted people.”

Child care is expensive because it is labor intensive. Many centers spend half or more of their budget on wages, so raising pay has a major financial impact. Under the Democrats’ plan, the federal government would cover all new costs for the first three years, but states would then pay 10 percent.

How much Democrats would raise pay remains unclear. The House bill says child care workers should receive a “living wage,” which it does not define, but also says they should be paid the same as elementary educators with the same credentials, a different standard.

Other uncertainties remain. Mr. Biden proposed subsidies for about three-quarters of households, excluding the most affluent. But the House version covers everyone.

Beyond legislative detail, progressives are seeking a paradigm shift. They see child care much like public education: a service on which society depends and therefore should ensure.

“It’s a public good and should be treated that way” said Julie Kashen, a senior fellow at the Century Foundation. “The shared stake in seeing children thrive doesn’t suddenly begin when they turn five.”

But conservatives fear government intrusion into the family realm. Rachel Greszler, an analyst with the Heritage Foundation, recently warned Congress that the measure would increase costs and drive small centers out of business, especially those based in homes and churches. She also said the policy would penalize parents who stay at home, taxing them to expand center-based care and ignoring the “tremendous personal and societal value” of full-time child-rearing.

Ms. Lolley said she thought about staying at home after having a second child but needed the health insurance that came with her job.

“Oh my God, it was terrible,” she said of the cost, more than $20,000 a year, of having two children in care. She hung on with significant help from her parents, knowing that “we wouldn’t have a kid in day care forever.” Most Greensboro parents, asked about the bill, agreed the problem it tackles are serious, but their views of federal help varied.

“I’d love for this to pass,” said Melissa Robertson, a freight broker, after hearing a summary of the legislation. She and her wife said their two children are thriving at the Wishview Children’s Center, but it costs twice as much as their mortgage, and a shortage of infant care causes Ms. Robertson to work from home several days a week.

“It can be kind of difficult when you’ve got a screaming baby in the background,” she said. “Sometimes clients are like, ‘Oh, can’t you get them into child care?’” With two working parents the norm, she said, “We should be able to provide child care.”

But another Wishview parent, Jamie Pritchard, had reservations. She and her husband, Matt, who work at the same insurance firm, have three children in care and pay about $34,000 a year. “Basically, my paycheck goes to pay for child care,” she said.

Still, she warned subsidies could lead to higher taxes. “If we were not financially stable, we would be all for that,” she said. “But I always think that if we’re getting help, the money has to come from somewhere.”

Ms. Lolley knew nothing of the plan until a reporter described it and reacted with enthusiasm tinged with concern. She praised the potential financial relief and the “wonderful” help for teachers, whom she called devoted and “very underpaid.”

But she also noted that federal money often brings federal rules.

“If it would make things worse for the school in any way,” she said, “I personally would rather stretch to keep paying the bills.”