WATERLOO, Iowa—Erin Turner recently started working 12-hour shifts to cover the $1,520 a month she spends on child care for her two young children, more than twice her rent. She says she sometimes eats crackers for dinner because money is so tight.

“We’re already living within our means. We don’t have anywhere else to cut back,” said Ms. Turner, 30 years old.

In...

WATERLOO, Iowa—Erin Turner recently started working 12-hour shifts to cover the $1,520 a month she spends on child care for her two young children, more than twice her rent. She says she sometimes eats crackers for dinner because money is so tight.

“We’re already living within our means. We don’t have anywhere else to cut back,” said Ms. Turner, 30 years old.

In Iowa and around the country, in blue and red states alike, the cost of child care is weighing down families, one of several compounding problems in a sector that politicians of both parties agree is in need of reform.

Some families spend nearly one-third of their income on child care. Parents are competing for limited options. As more people leave the workforce or demand higher pay, child-care centers can’t find staff willing to work for little more than minimum wage.

The rapid spread of the Omicron variant is making things worse. Parents, children and child-care providers are contracting the virus in record numbers, further straining the economy.

Democrats and Republicans in Washington say they recognize the problem, but disagree on the solutions. The prospect of a remedy from the narrowly divided Congress remains a long shot, but some lawmakers have said there is enough common ground to forge bipartisan compromise.

Democrats have proposed spending hundreds of billions of dollars to remake the country’s child-care system, which they describe as the biggest federal child-care investment in history. Their proposal would subsidize child care for many Americans, while seeking to raise wages for workers, increase the number of child-care providers and improve the quality of care.

Some families spend nearly one-third of their income on child care. A child-care facility in Waterloo, Iowa.

“It can make it possible for people who might be on the margin now between working and not working to make that decision to be in the labor force or be in the labor force for longer hours,” Heather Boushey, a member of the White House Council of Economic Advisers, said of the Democrats’ proposal. “Over time, that’s going to have significant effects on family income.”

But the Democrats’ plans, which are included in broader education, healthcare and climate-change legislation, are stalled in the Senate after Sen. Joe Manchin

raised concerns about the overall spending levels in the bill.

President Biden and his allies in Congress are working to revive the legislation. Some Democrats said they believe the West Virginia Democrat broadly supports the child-care provisions in the package, raising the prospect that a version of the measure could remain in a stripped-down compromise bill. Mr. Manchin’s office didn’t respond to requests for comment. The House passed a version of the legislation last year.

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Mr. Manchin’s vote in the 50-50 Senate is key because Democrats hope to pass their social-spending legislation without Republican support. Senate Republicans are unanimously opposed to the broader social-spending package and some have specifically criticized the child-care proposal, arguing it could end up making it harder for families to find care. If the measure does pass, some GOP governors could choose to opt out of the program.

“It fundamentally falls short of delivering expanded choice and affordability for our American families,” Sen. Joni Ernst,

an Iowa Republican, said during a recent event on the proposal.

Ms. Ernst and other Republicans in Congress have proposed several child-care measures, but the GOP hasn’t coalesced around one plan. GOP lawmakers have called for expanding tax credits to employers who provide on-site care and giving child-care providers additional support through grants and Small Business Administration programs.

Iowa exemplifies the problems playing out around the nation. The number of child-care programs in the state decreased by 56% during the last decade, and the number of available spaces for children dropped by 6%, according to data compiled by Iowa Child Care Resource and Referral, a nonprofit that provides child-care consultation, technical assistance and training. Child-care workers make as little as $8-to-$10 an hour.

Judy Wolf,

president of the Marita Theisen Childcare Center in Dubuque, said most of her new workers have quit within 90 days because they can make more money working at McDonald’s or Walmart.

Under the Democrats’ proposal, an eligible family of four in Iowa making $68,568 or less wouldn’t pay for child care. A family making $114,280—125% of the state median—would pay about $4,571 a year, or 4% of their income. A family making more than $228,560—250% of the median—would pay for the full cost of child care out of pocket.

To qualify for the subsidies, parents must be working or engaged in other activities like going to school.

The legislation also seeks to expand the market of licensed child-care providers; by some estimates, more than half of the U.S. population lives in areas without enough licensed facilities.

Erin Turner recently started working 12-hour shifts to cover the $1,520 a month she spends on child care for her two young daughters.

Brittany Graham, 29, spent more than four months looking for child care for her 1.5-year-old daughter. Open spots are so hard to find in this part of northeastern Iowa that she is coordinating with her child-care provider about when she should have a second baby.

She said she was the 120th person on a waiting list at one day-care center. “By the time you give me a call, my child won’t be an infant anymore,” Ms. Graham said she told workers at the center.

The Democrats’ legislation includes direct grants for establishing new child-care facilities, as well as for expanding and improving existing ones. It would also provide grants for increasing the pay of child-care workers and providing professional development and training. The grant programs would largely be left up to states to design.

The proposed subsidies in the legislation would likely result in a surge in demand for child care, according to economists. If that surge isn’t accompanied by a corresponding increase in child-care providers, the effort could lead to renewed scarcity and price increases for those who don’t qualify for subsidies, some economists said.

In an effort to combat potential price jumps, the legislation phases in the subsidies over three years to allow for the gradual development of new child-care centers that can meet the increased demand. On the first day the program goes into effect, 13 million children from low- and middle-income families would be eligible for the subsidies, Democrats said.

Janet Currie, a Princeton University economist who specializes in families and children, said small child-care programs could be set up quickly, but it will take longer to establish larger child-care facilities that meet state and federal requirements.

“We have a better idea of how subsidies are going to affect demand than we do about how the largely unspecified things to increase supply are going to work,” she said.

By some estimates, more than half of the U.S. population lives in areas without enough licensed child-care facilities. A child-care center in Waterloo, Iowa.

Republican lawmakers argue that the Democratic proposal could hurt wealthier U.S. families and impose burdensome quality standards on child-care facilities. Some Republicans have also criticized language in the bill mandating that grant funding for updating facilities shouldn’t be used to improve facilities that are primarily for religious worship.

Democratic aides note that the legislation includes language specifying that the subsidies can be used at all licensed child-care facilities, including those associated with religious groups. The restrictions on facilities grants are intended to prevent religious groups from using the money to, for example, replace the pews in a church instead of the child-care center in the church’s basement, the aides said. Roughly 15% of working U.S. parents use faith-based child-care centers, according to a 2020 survey.

The architects of the legislation say it would help the majority of working families afford quality care and open a path for women, who disproportionately bear the burden of child care, to re-enter the workforce.

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“We have built this very carefully,” said Sen. Patty Murray (D., Wash.), a lead advocate for the child-care provisions, adding that the legislation was designed to prevent price increases.

Iowa Gov. Kim Reynolds, a Republican who launched a task force to address problems with child care in her state, opposes the Democrats’ child-care proposal, according to a spokesman for her office.

The spokesman said it is premature to say whether Ms. Reynolds would opt out of the child-care program if it passes. If states choose to opt out of the program, localities can apply directly to the federal government for the new funding provided in the bill.

Ms. Turner, meanwhile, found herself facing stacks of new bills after her husband transitioned from active duty military to the national guard. Military benefits had helped the family pay for housing and food. She now works 5:30 a.m. until 5 p.m., five days a week to narrow the gap.

“I’m praying those extra hours are going to cover it,” she said. “We don’t have options right now.”

Democrats have proposed spending hundreds of billions of dollars to remake the country’s child-care system. A child-care center in Waterloo, Iowa.

Write to Andrew Restuccia at andrew.restuccia@wsj.com