WASHINGTON — A divided House on Tuesday approved a $3.5 trillion budget blueprint that would pave the way for a vast expansion of social safety net and climate programs, as Democrats overcame sharp internal rifts to advance a critical piece of President Joe Biden’s ambitious domestic agenda.

Approving the budget was a major step in Democrats’ drive to enact their top priorities — including huge investments in education, child care, health care, paid leave, and tax increases on wealthy people and corporations — over united Republican opposition. With a single vote Tuesday, they laid the groundwork to move quickly on legislation that would accomplish those goals, setting a late-September deadline for action on a $1 trillion bipartisan infrastructure package.

But it came only after leaders stamped out a revolt among conservative-leaning Democrats, who withheld their votes until they extracted a promise to vote on the infrastructure bill by Sept. 27. The breakthrough came after a pressure campaign by the White House, outside progressive groups and Speaker Nancy Pelosi of California, who haggled and cajoled her way to unanimous Democratic support for a measure that had been stalled mere hours before.

The vote was 220-212 on party lines to approve the budget plan and allow future votes on both the infrastructure bill and a voting-rights measure that the House passed soon after.

Although the budget plan, which passed the Senate this month, does not have the force of law, it allows Democrats to move forward with a fast-track process known as reconciliation. That would enshrine the details of the blueprint in legislation that is shielded from a filibuster, allowing it to pass over the objections of Republicans.

It is expected to include universal preschool, paid family leave, federal support for child care and elder care, an expansion of Medicare and a broad effort to tackle climate change — all paid for through tax increases on high earners and companies.

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“Today is a great day of pride for our country and for Democrats,” Pelosi declared on the House floor, after days of intensive talks with rank-and-file lawmakers. “Not only are we building the physical infrastructure of America, we are building the human infrastructure of America to enable many more people to participate in the success of our economy and the growth of our society.”

Speaking at the White House shortly after, Biden called Pelosi “masterful,” and lavished praise on the party’s leadership team and every congressional Democrat who ultimately supported the legislation.

“There were differences, strong points of view — they’re always welcome,” Biden said. “What is important is that we came together to advance our agenda.”

But the herculean effort it took to do so only served to illustrate the difficult road ahead for Biden’s agenda on Capitol Hill, where Democrats’ small majorities and ideological divisions — as well as Republican opposition — have left the party with little room to maneuver.

The same differences between moderates and progressives that nearly derailed the plan this week promise to resurface in the weeks to come, as progressives push to make the reconciliation bill as far-reaching as possible and conservative-leaning Democrats work to limit its scope.

In a joint statement, Rep. Josh Gottheimer, D-N.J., and eight other moderates who had conditioned their votes for the budget on a deadline for action on infrastructure boasted that their group had succeeded in making sure that the bipartisan bill would “receive stand-alone consideration, fully de-linked, and on its own merits.”

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But moments after the budget plan passed, a large group of liberal Democrats signaled that they still regarded the two measures as linked, raising the prospect of another standoff next month.

“As our members have made clear for three months, the two are integrally tied together, and we will only vote for the infrastructure bill after passing the reconciliation bill,” Rep. Pramila Jayapal, D-Wash., leader of the Congressional Progressive Caucus, said in a statement

)In the evenly divided Senate, leaders need the votes of every Democrat and independent — plus Vice President Kamala Harris, who can break ties — to win passage of the reconciliation bill. In the House, the margin is only slightly more forgiving, allowing as few as three Democrats to defect if all Republicans are opposed, as expected.

The commitment to a Sept. 27 vote on the bipartisan infrastructure package added to a chaotic series of deadlines next month, when lawmakers will have only a few days in Washington to consider the infrastructure bill, prevent a lapse in government funding Oct. 1 and steer the government away from the brink of a catastrophic debt default by raising the statutory limit on the nation’s borrowing. Party leaders have instructed committees to finish writing pieces of the reconciliation package by Sept. 15, although it is unclear whether they will be able to do so.

For now, the deal that Pelosi struck amounted to a precarious detente for Democrats that did nothing to resolve tensions between the moderate and liberal flanks or end the jockeying for political leverage.

The divisions began to flare this month, when nine centrist Democrats publicly announced that they would not advance the budget blueprint until the House passed the Senate-passed bipartisan infrastructure agreement, which omits many of the party’s highest priorities. Liberals called the compromise insufficient.

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Pelosi had already said she would not move the infrastructure bill, which includes $550 billion in new funding for roads, bridges, water and climate-resiliency projects, until the reconciliation bill passed.

That led to a stalemate this week, as Pelosi called the House back for a rare summer session.

In a series of phone calls and private meetings that stretched past midnight Monday, Democratic leaders sought to persuade their colleagues to drop their insistence on passing the infrastructure bill first. They did so after securing a hard commitment, enshrined in legislation, that a vote would come on or before Sept. 27.

Ultimately, Pelosi also pledged that the House would vote only on a reconciliation package that could clear the Senate, sparing moderate lawmakers tough votes on provisions that could never become law

)Rep. Stephanie Murphy, D-Fla., who joined her party’s holdouts Monday, said the negotiation showed that centrists were willing to use their sway in the House.

“I think what it is a sign of is that moderates are serious about legislating in a responsible, transparent, inclusive way,” Murphy said before the vote, adding that she had personally sent a list of proposed changes to Democratic leaders to ensure moderate support.

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But the episode was grueling for all involved. Asked early Tuesday whether the agreement was a win for Gottheimer, Pelosi responded with an incredulous “a win?”

A weary Rep. Jim McGovern, D-Mass., chair of the Rules Committee and who convened his panel three times in two days as the talks dragged on, said he had had enough.

“I love you all, but I’m done, and we should move forward and not meet again for a while,” McGovern told lawmakers on the committee.

Yet despite the potentially messy path ahead, leading Democrats said they were confident that Biden’s agenda would emerge from Congress intact, even as moderate senators push to rein in the overall price tag.

“Both are going to pass, whatever the sequence,” said Rep. Steny Hoyer of Maryland, the No. 2 Democrat.

But progressive lawmakers remain concerned that if the reconciliation bill did not go first, provisions addressing climate change, paid family leave, health care and educational opportunity could fall by the wayside, lacking enough support to be enacted into law.

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Many faulted their conservative-leaning colleagues for threatening to derail the budget plan and said no deadline would be enough to separate the infrastructure bill from the budget legislation.

“The whole thing was a fiasco, to be honest,” said Rep. Ilhan Omar, D-Minn., whip of the Progressive Caucus. “The commitment still is there for us to follow through the strategy of having both of these pieces of legislation simultaneously move together.”

Although some Republicans are expected to support the bipartisan infrastructure bill, they were uniformly opposed to the budget blueprint, citing concerns about its size, proposed tax increases and the possibility that the additional spending would worsen inflation. The House Republican campaign arm began targeting the moderate lawmakers who had ultimately backed the budget, saying the vote “proves they’re willing to sell out their constituents.”

“A budget is supposed to put Washington on a sustainable fiscal path and help the American people keep Congress honest about its spending,” said Rep. Jason Smith, R-Mo., the top GOP member on the Budget Committee. “Unfortunately, Washington Democrats are using the budget as a political tool to unleash trillions in new spending and taxes and enact misguided policies.”This article originally appeared in The New York Times.