To meet as many political priorities as possible and keep the price tag low, Democrats have funded numerous programs, including an expanded child tax credit, a universal preschool program, and short-term health care grants. For most Democrats, it was a way to please multiple constituencies, show progress on long-term goals, and bet future congresses would expand the agendas. For Mr. Manchin, it was an unacceptable budgetary gadget.

Now, as President Biden and the Main Democrats try to save the bill and get the necessary support from Mr Manchin in the Senate at 50-50, they are grappling with the possibility of removing valuable priorities and fund fewer programs for longer periods.

“There are specific issues that have been raised that we can resolve. Others get to the heart of the bill and are much more difficult to resolve, ”said Sen. Chris Van Hollen (D., Md.). “If the goal is to extend each program in the bill for a full 10 years, that would prevent us from doing a lot of other pieces.”

Democrats had hoped to complete the bill this year, but continued negotiations with Mr Manchin and parliamentary challenges leave lawmakers to expect additional weeks of work.

Mr Manchin set a cap of $ 1.75 trillion for the decade-long bill. This has already prompted Democrats to set expiration dates for the programs to reduce the overall cost. He also opposes the combination of temporary programs and permanent sources of income, calling it a gimmick that hides the true expected cost.

Democrats broadly accept this $ 1.75 trillion level and the accompanying tax increases. But the bill the House passed in November is chock-full of temporary programs, including an expanded child tax credit that would expire after just one year, after 2022. They have said they will pay for future extensions.

To address Mr Manchin’s concerns, Democrats could sharply reduce the expansion of the child tax credit. Alternatively, they could get this credit to consume a larger slice of the $ 1.75 trillion pie, putting limits on climate change, pre-kindergarten, childcare and healthcare policies and endangering the support they have garnered from party factions that focus on these issues.

Lawmakers have been flexible throughout the year. They envisioned a $ 3.5 trillion package, but scaled it back to appeal to Mr. Manchin and Senator Kyrsten Sinema (D., Arizona). They have scrapped proposals – including two years of free community college, 12-week paid leave, and a program pushing utilities to rely on clean energy – to lower the price. They abandoned a planned increase in the highest tax rates that Ms Sinema opposed.

Now Democrats are rushing to use their narrow margins in the House and Senate to push through some of Mr. Biden’s key campaign proposals ahead of the midterm elections that could end those majorities.

“If they don’t, it would be one of the biggest goals in legislative history,” said Ben Koltun, research director at Beacon Policy Advisors. “They basically have the vehicle, the ship, the pay-for. And it is on all the goodies that they must agree. That’s why I’m pretty optimistic that they’ll get there.

However, doing what Mr. Manchin wants could force a drastic redefinition of priorities.

Mr Biden said Thursday he would have further talks with Mr Manchin. The president’s statement scanned the policy areas of the bill, listing climate change, prescription drug prices, health care, elderly care and child care and giving no indication of what might be reduced.

“We need presidential leadership. It’s up to President Biden to say, this is what I want the policies to be that will fit into this package, ”said Ben Ritz of the Progressive Policy Institute, a center-leaning Democratic think tank. “President Biden is the only person who can make this call and get away with it.”

Mr Manchin said he was waiting for his colleagues to produce a comprehensive bill. This is stuck in parliamentary demands and disagreements over national and local tax deduction.

“At this point it’s kind of a moving target when it comes to Joe and Kyrsten,” said Senator Tammy Duckworth (D., Ill.)

What could the Democrats do?

A full 10-year version of the child tax credit expansion Congress passed in March could approach $ 1.6 trillion, consuming almost all of the $ 1.75 trillion space Mr. Manchin had would allow. Almost half of that extends the credit boom Republicans passed in 2017, which is set to expire after 2025.

Democrats have cheaper options. They could extend the credit features that give the full benefit to low-income households without keeping the credit increase from $ 2,000 to $ 3,000 for most children and $ 3,600 for those under 6 years of age. They could continue repealing personal exemptions beyond 2025 to offset the credit.

Sometimes Mr. Manchin criticized the size of the loan and asked for work requirements for the beneficiaries. Recently, he stressed his credit support and focused on his concerns about the temporary expansion.

Major credit advocates including Sen. Michael Bennet (D., Colorado) and Sherrod Brown (D., Ohio) support the changes. In their view, the extended credit was a generational achievement in reducing child poverty — one that Mr. Manchin voted for in March — and should not be changed.

Removing other provisions could be just as difficult, as each satisfies a different faction of the Democratic coalition.

When asked which parts of the bill should change, Sen. Bernie Sanders (I., Vermont) said, “If we do, we’ll make them more progressive.”

This question of priorities – little for longer periods or many things temporarily – has been at the center of the Democrats’ internal strife.

By the end of October, it looked like they had solved these issues. Mr. Biden released a framework from meetings with Mr. Manchin and Ms. Sinema. The White House said it was confident the House and Senate could adopt this version.

That assurance was enough to get the bill drafted and passed in the House. Representative Pramila Jayapal (D., Wash.), Who heads the Progressive Congressional Caucus, said Thursday the House passed it on the basis of Mr. Biden’s promise that he could deliver 50 votes in the Senate.

But the framework did not really address Mr Manchin’s concerns, and it did not have the broad buy-in that was intended, Mr Ritz said. Democrats must now take this into account. “We bit more than we could chew and now we’re choking,” Mr. Ritz said.

Write to Richard Rubin at richard.rubin@wsj.com and Andrew Duehren at andrew.duehren@wsj.com