WASHINGTON—Choosing which Americans should be eligible for benefits in a proposed expansion of the social-safety net is one of the main challenges vexing Democrats, who are attempting to slim down their healthcare, education, child-care and climate bill in the coming weeks.

The debate over whether to provide the benefits to low-income Americans only or a broader swath of the public comes as Democrats work to unite their progressives and centrist wings around a revised package. So-called means-testing is one of several methods...

WASHINGTON—Choosing which Americans should be eligible for benefits in a proposed expansion of the social-safety net is one of the main challenges vexing Democrats, who are attempting to slim down their healthcare, education, child-care and climate bill in the coming weeks.

The debate over whether to provide the benefits to low-income Americans only or a broader swath of the public comes as Democrats work to unite their progressives and centrist wings around a revised package. So-called means-testing is one of several methods Democrats are considering for reducing the price tag of the $3.5 trillion proposal, along with potentially dropping some programs altogether or reducing the number of years funded.

“We have some important decisions to make in the next few days,” House Speaker Nancy Pelosi (D., Calif.) said at a press conference Tuesday.

On one side of the debate over means-testing are Democrats like Sen. Joe Manchin (D., W.Va.) who want to target the government aid to low-income Americans, arguing that narrowing eligibility for the programs to those most in need will be a cheaper and more efficient use of taxpayer funds.

On the other side are both progressive and centrist Democrats who want to make programs like subsidized child care, free preschool and two years of free community college available to Americans up and down the income ladder. Invoking the legacies of Social Security and Medicare, each decades old and broadly available to Americans, these Democrats view universal programs as both more effective at helping Americans in need and better at winning enduring political support.

Mrs. Pelosi hasn’t indicated where she stands on income eligibility. She said this week that Democrats could pare back the number of programs while also looking at reducing the number of years funded, to bring down the price of the bill.

“Overwhelmingly, the guidance I am receiving from members is to do fewer things well,” she said in a letter Monday, without elaborating on what could be on the chopping block. When pressed Tuesday about possible cuts, she said, “Mostly we would be cutting back on years and something like that.”

House Speaker Nancy Pelosi, speaking in Washington on Tuesday, hasn’t indicated where she stands on income eligibility.

Photo: JAMES LAWLER DUGGAN/REUTERS

Mr. Manchin has said he supports $1.5 trillion of spending, far below the $3.5 trillion in spending Democrats had originally outlined. President Biden has recently told House Democrats he expects the final price tag to land around $2 trillion, kicking off a scramble to find hundreds of billions of dollars of spending to cut from the party’s marquee bill.

“We’re having important discussions about what a package that is smaller than $3.5 trillion would look like,” White House press secretary Jen Psaki

said Tuesday. “What we have to do is work with a range of members who have a range of views about what should be included in a package,” she said.

Democrats are using a process called reconciliation to advance the bill through the 50-50 Senate with just a simple majority, rather than the 60 usually required. No Republicans are expected to support the bill, calling it wasteful and potentially damaging to the economy, meaning Democrats can’t afford to lose a single vote in the Senate, or more than three in the House.

How Democrats ultimately resolve the debate is set to establish whether many Americans can access the bevy of proposed programs—and shape the party’s electoral success in 2022.

“I think it creates more buy-in when we’re investing in a large number of Americans,” said Rep. Conor Lamb

(D., Pa.), a centrist running for Senate, arguing that universal programs will better resonate with voters ahead of the 2022 midterms. But he acknowledged it is still an unsettled question.

“Both sides of the debate are arguing that their approach is going to be better at election time,” he said.

Not only does narrowing eligibility for the bill’s programs lower its cost, it could also help Democrats ward off political attacks that they are spending money on Americans who don’t need it.

Rep. Jared Golden (D., Maine), who represents a competitive district, wrote in a recent op-ed in the Portland Press Herald that the bills’ programs should be “responsibly targeted to working and middle class families.” Mr. Manchin has repeatedly warned against the creation of an “entitlement society.”

Max Sawicky, a senior research fellow at the Center for Economic and Policy Research, a liberal think tank, said means-testing programs will help build political support for the bill.

“The details of any scheme like that are basically lost on voters, but hearing that it’s not a freebie for everybody lets members like Manchin say, ‘We didn’t give away the whole store, we injected discipline into the program,’ ” Mr. Sawicky said.

While providing the benefits of the bill to only low- and middle-income Americans may prove politically helpful to pass the bill in the short term, it could pose a political problem in the long term, according to Molly Michelmore, a history professor at Washington & Lee University who studies U.S. fiscal policy.

Ms. Michelmore said Social Security and Medicare have persisted for decades because many Americans pay into and benefit from them, making it politically difficult for lawmakers to try to cut them. An AARP poll from 2020 showed Social Security with more than 90% support across political parties.

Social programs in the U.S. targeted to poor Americans have historically been more vulnerable to cuts and political attack, she said, pointing to the 1996 welfare reform bill.

“Having that means-tested is going to reduce the constituency for that program and really make it feel much more like welfare, which is politically toxic,” Ms. Michelmore said.

Unlike Social Security and Medicare, though, the social programs in Mr. Biden’s agenda would be funded by tax increases on the wealthy and businesses, rather than payroll taxes.

The debate among Democrats has cut across typical ideological lines, with centrist and moderate Democrats lining up in favor and against means-testing elements of the bill. Centrists like Mr. Lamb who favor universal benefits have also pushed for the legislation to focus resources on a smaller number of programs over the long term. Progressives have advocated that Democrats fund a range of universal programs for a shorter number of years and put pressure on future lawmakers to keep funding the benefits.

Some Democrats and outside advocates also argue that means-testing programs harm their efficacy. Requiring Americans to prove their eligibility can create barriers to entry, reducing participation rates. The earnings of lower-income Americans is sometimes unstable, meaning some people could shift in and out of eligibility over the course of a year, they say.

“When you wave your hands and say we’re going to have means-testing, the details matter enormously,” said Elizabeth Lower-Basch, the director of income and work supports at the Center for Law and Social Policy.

—Catherine Lucey contributed to this article.

Write to Andrew Duehren at andrew.duehren@wsj.com