In failing to secure a benefit with bipartisan appeal, President Biden joins a long line of frustrated politicians. But some Republicans say it could be resurrected on its own.WASHINGTON — In late 2019, with bipartisan backing, including from the iconoclastic Senate Democrat Kyrsten Sinema of Arizona, President Donald J. Trump’s daughter Ivanka hosted a summit at the White House to promote her vision for paid family and medical leave.As with many domestic initiatives of the Trump years, the effort went nowhere, thanks in part to the former president’s lack of interest in legislating. But it also stalled in part because of opposition from Democrats like Senator Kirsten Gillibrand of New York, who saw the plan not as a true federal benefit but as a “payday loan” off future Social Security benefits.Ms. Gillibrand believed she could do much better.Last week was the Democrats’ turn to fail. A 12-week paid family and medical leave program, costing $500 billion over 10 years, was supposed to be a centerpiece of President Biden’s social safety net legislation. But it fell out of his compromise framework, a victim of centrists who objected to its ambition and cost.The demise of the effort, even amid bipartisan interest, in part reflected the polarization surrounding Democrats’ marquee domestic legislation, which Republicans are opposing en masse.Some business groups and G.O.P. proponents of a paid leave program believe that if it had been broken out and negotiated with Republicans, the way a $1 trillion infrastructure package was at Mr. Biden’s urging, it could have survived, and some think it still could resurrected as a bipartisan initiative.They said the problem lay with the Democrats’ decision to put paid family leave in the expansive social policy and climate bill — a multitrillion-dollar package financed by large tax increases on businesses and the wealthy — which they knew that Republicans and mainstream business groups would never support.“In any area that is substantive, when members sit down to actually walk through whether or not we can build good legislation, there are possibilities,” Senator Lisa Murkowski, Republican of Alaska, said. “We’re not being encouraged to work together to solve problems. What we’re being encouraged to do is line up with the team so that we can have the political messaging point.”At least for now, though, the United States is almost certain to remain one of only six countries with no national paid leave.“Fundamentally, to provide paid leave, you have to value women and value their work,” Ms. Gillibrand lamented, “and valuing women and their work is a hard thing for the United States.”The last-minute removal of the paid leave program underscored longstanding questions about how it can be that while 186 other countries have such a program, the United States does not.A rally for paid leave near the White House. The United States is one of only six countries that do not provide some sort of national paid leave.Valerie Plesch for The New York TimesMs. Gillibrand was highly skeptical that a bipartisan deal to address the issue was possible. She said she had been developing paid family and medical leave legislation for nearly a decade, had sought out numerous Republican and business partners, and had always found the parties too ideologically divided.But the issue driving interest in both parties — bringing more women into the work force and keeping them there — has only grown more acute since the coronavirus pandemic hit.White House officials say 95 percent of the lowest-wage workers lack any paid leave, and they are predominantly women and people of color. Some five million women lost their jobs during the pandemic, and many of them, struggling with access to child care and bedeviled by intermittent school closures and periodic Covid-19 outbreaks, have opted not to return.Mr. Trump campaigned on the issue and included six weeks of federally paid leave in his budgets, which were ignored by Republican leaders. Congressional Republicans had their own ideas. Legislation introduced in 2019 by Senators Sinema and Bill Cassidy, Republican of Louisiana, and Representatives Elise Stefanik, Republican of New York, and Colin Allred, Democrat of Texas, would offer new parents $5,000 during the first year of their baby’s life, which they would repay over the decade through cuts to their child tax credit.The Republican senators Marco Rubio of Florida, Mitt Romney of Utah, Joni Ernst of Iowa and Mike Lee of Utah similarly proposed offering workers parental leave benefits that would have to be repaid — with interest — through cuts in their Social Security retirement benefits.Senator Deb Fischer, Republican of Nebraska, championed and secured more modest legislation — tucked into the Republican tax cuts of 2017 — that gave small businesses a tax credit to fund family leave. She argued against broader versions, since many companies already offer employees paid leave.“If you have two or three employees, you cannot afford to do paid family leave because you can’t afford to hire somebody to take their place, which is why I think the tax credit that we have in law now is really beneficial,” Ms. Fischer said.According to the White House, fewer than a third of small businesses with 100 or more employees offer paid leave. Only 14 percent with fewer than 50 employees do. Ms. Fischer conceded that few small businesses have taken advantage of her credit, but she blamed the Treasury Department, under Mr. Trump and Mr. Biden, for dragging its feet on issuing detailed regulations and promoting it.To Democrats, those proposals are not true leave. They are either loans off other needed benefits or too limited to make a difference. Ms. Gillibrand said that optimally, a stable, generous family and medical leave plan would be an “earned benefit” like Social Security and Medicare: Workers would pay into the system and claim the benefit when they needed it, regardless of where they worked or how much they earned.But, she said, taxing workers has become politically difficult. Her 2013 bill envisioned family and medical leave insurance, financed by a small contribution from employers with each paycheck.This year, the Biden administration and Democratic leaders opted to fund paid leave out of general revenues, bolstered by tax increases on the wealthy and corporations. They said the program was part of a broader “human infrastructure” effort to help children and young parents, which included child care support, a child tax credit and universal prekindergarten — and therefore didn’t need a dedicated funding source.Senator Joe Manchin III, Democrat of West Virginia, opposed a plan for 12 weeks of paid family and medical leave, saying he worried that without a stable revenue source, it would be a drain on the Social Security system.Al Drago for The New York TimesThe House proposal would have guaranteed 12 weeks of paid family and medical leave annually to all workers, in private or government employment, gig work like Uber and Lyft, or self-employment. The benefit would have replaced 85 percent of wages or earnings for the lowest-paid workers, scaling back from there.That generosity was why the plan ran into a roadblock in the Senate. Senator Joe Manchin III, Democrat of West Virginia, saw an expensive new benefit without a stable revenue source that he worried would end up draining an already stressed Social Security system.Ms. Gillibrand and Senator Patty Murray, Democrat of Washington, have pleaded, cajoled and bargained with him. They said a paid leave plan would actually bolster Social Security’s finances by helping women get back to work, where they would pay Social Security taxes, and helping young families have more children, which would bolster the work force of the future. Democrats offered to scale back a 12-week leave plan to four weeks, then to limit it to leave for new babies, not medical emergencies.Mr. Manchin promised to consider the offers, but few are optimistic. Ms. Gillibrand sees societal issues at work. While it is true that virtually every country in the world has a paid leave program, that is somewhat misleading, she said.Most of those countries can afford to offer paid leave because they do not actually expect women to work once they begin having children. Long leave plans help couples get started having children, but most countries then do not help with child care because they assume women will stay home.The U.S. work force relies on women. Mr. Biden’s compromise framework does include generous subsidies for child care starting at birth and for universal prekindergarten for 3- and 4-year-olds. It now lacks the first step: helping parents through pregnancy and childbirth.“What we’re trying to achieve here is the ability of women to work effectively and to be most productive at work,” Ms. Gillibrand said.Advocates say lawmakers should not give up yet. Marc Freedman, the U.S. Chamber of Commerce’s vice president for employment policy, said the business group had been meeting with congressional offices before the pandemic, pressing for a national paid leave plan to replace the patchwork of state and local government plans popping up.The government would create a minimum benefit that businesses would be allowed to exceed for recruitment and retention, financed by a payroll tax paid by employees. Such a plan would help smaller businesses compete for labor with larger corporations, while offloading some of the burden on companies that already offer leave plans.“We very much want to restart those conversations,” he said.Some Republicans, especially Republican women, say they are ready to join those talks.“It’s an issue we need to address as a nation and look at and get creative with,” said Senator Shelley Moore Capito, Republican of West Virginia, who helped secure paid leave for federal workers.But as with the infrastructure deal struck over the summer, Democrats would not be likely to get all they want. Ms. Capito, for instance, said the plan that Mr. Manchin killed was too generous, with leave beyond care for new babies and sick family members.Ms. Gillibrand said she had already begun outreach. She talked to Senator Susan Collins, Republican of Maine, about an interim step of helping small states pool with larger ones to create regional leave programs. She signaled flexibility on funding the kind of insurance mechanism that Mr. Freedman said the Chamber of Commerce favored.But none of those ideas would happen as quickly as the broad program that Mr. Manchin is opposing, she said.“There is work I can do over the next six months to a year, sure, but will take time,” Ms. Gillibrand concluded. “And it won’t be simple.” More