WASHINGTON — Facing resistance by a group of moderates in their ranks, Democratic leaders put their $1.85 trillion social policy, climate and tax package on hold on Friday, instead pushing to pass a $1 trillion bipartisan infrastructure package whose fate was uncertain amid progressive opposition.

The retreat came after centrist Democrats balked at supporting the social policy plan without a formal estimate of its cost and economic effects. Hoping to convey movement toward approving it, House leaders said they would hold a procedural vote that would allow consideration of the measure in the future, with hopes of passing it by Thanksgiving.

But the delay and uncertainty were a setback for President Biden and Democratic congressional leaders, who had hoped to pass both measures on Friday and instead risked ending the day empty-handed, as intraparty feuding between moderates and progressives imperiled their agenda.

An off-year electoral drubbing this week further raised the stakes for anxious Democrats eager to prove that their party could deliver while in control of both chambers of Congress and the White House.

“Welcome to my world — this is the Democratic Party,” Speaker Nancy Pelosi of California told reporters at the Capitol as she announced the postponement of the social policy bill. “We are not a lock-step party.”

“It’s an additional challenge,” she added. “But I see every challenge as an opportunity.”

The most immediate question was whether the infrastructure legislation would have the votes to pass, as talks dragged into the evening. Liberal Democrats who have demanded that the two bills move in tandem indicated that they might oppose the infrastructure measure on its own. And while it was expected to draw some Republican support, it was not clear whether that would be enough to offset Democratic defections given the party’s slim margin of control.

Asked whether she had the votes to pass the infrastructure bill, Ms. Pelosi told reporters, “We’ll see, won’t we?”

The Congressional Progressive Caucus, whose members have refused to support the public works bill until they were certain the social policy bill was on track, huddled into the evening, ordering pizza delivered to the Capitol as they discussed whether to allow the infrastructure measure to proceed.

In a private show of hands, at least 20 of them indicated they were ready to oppose the bill without a vote on the social safety net package. Mr. Biden, who spent much of Friday calling individual lawmakers in an effort to salvage his agenda, later called into the meeting, where he was placed on speakerphone to make a plea for passage of the infrastructure bill.

The liberals were enraged after about a half-dozen moderates insisted that the social policy bill be delayed until they could obtain an official cost estimate from the Congressional Budget Office, the legislative scorekeeper on Capitol Hill.

“If our six colleagues still want to wait for a C.B.O. score, we would agree to give them that time — after which point we can vote on both bills together,” Representative Pramila Jayapal of Washington, the Progressive Caucus chairwoman, said in a statement.

The shift in strategy came despite public and private appeals from Mr. Biden. As Ms. Pelosi held a marathon round of meetings in her Capitol office to try to resolve the internal disputes, the president called lawmakers and pushed for a quick resolution on Friday.

Mr. Biden said at the White House that he was asking every House member “to vote yes on both these bills right now.”

He concluded with a succinct message for lawmakers: “Let’s get this done.”

He followed up with private calls to moderate skeptics balking at supporting the social policy bill. Later, Mr. Biden twice phoned Ms. Jayapal in an effort to ease passage of the infrastructure measure. He postponed a planned weekend trip to his home in Delaware as the negotiations stretched into Friday night.

For Mr. Biden, approval of both bills would be welcome progress at a vulnerable moment. The president’s approval ratings have declined in recent months amid concerns about increasing inflation, a persistent pandemic and the messy U.S. withdrawal from Afghanistan.

And he returned from an overseas trip this week to find grim political realities at home, after Republicans won the governor’s race in Virginia and came closer than expected to defeating the Democratic governor of New Jersey. The results underscored a sense of dread among Democrats who had already been bracing for losses in the 2022 midterm elections that would cost them control of Congress.

But if anything, the prospect of losses deepened the divisions imperiling both pillars of the Mr. Biden’s agenda. House leaders started the day aiming for votes to advance the social policy bill and clear the infrastructure measure — the largest investment in the nation’s aging public works in a decade — for his signature.

But by midday, their efforts had stalled as a 15-minute House vote dragged on more than seven hours — a record, lawmakers said, for the longest vote in the chamber — as Ms. Pelosi toiled to line up support. Republicans, united in opposition to the social policy bill and gleeful over the chaos, forced additional procedural votes to further derail the process.

“Where are the Democrats today?” said Representative Kevin McCarthy of California, the minority leader. “Breaking their own rules, setting new records just keeping votes open, and trying to intimidate and bully their own members to vote for something.”

The delay felt painfully familiar to Democratic lawmakers and Mr. Biden, who have tried and failed twice in the past several weeks to push the pair of bills through the House, only to see their plans impeded by internal divisions. Yet there was little indication that the personal outreach from Mr. Biden and House leaders had resolved the deep mistrust between the ideological factions of the party.

At least four House Democrats — Representatives Jared Golden of Maine, Kurt Schrader of Oregon, Ed Case of Hawaii and Stephanie Murphy of Florida — were demanding an official cost analysis from the Congressional Budget Office before voting on the social safety net package. That would be enough Democrats to derail the legislation if, as expected, every Republican opposed it.

Democratic leaders tried to use an analysis by the nonpartisan Joint Committee on Taxation and a White House analysis of the spending costs to win over the holdouts, to no avail. Top White House aides were seen entering Ms. Pelosi’s office as party leaders struggled to win over the moderates.

“It’s a very difficult task, and we’re working on it,” said Representative Steny H. Hoyer of Maryland, the majority leader, as he brushed away questions Friday about whether Democrats would have the necessary votes.

Eventually, top Democrats pulled back on their plans to march forward on the social policy bill and instead signed onto a plan proposed by leaders of the Congressional Black Caucus to shelve it and move to a vote on the infrastructure plan. They would first take a procedural vote on the safety net and climate plan that would pave the way for considering it later — a show of “good faith,” its proponents said, according to a person with knowledge of discussions within the Congressional Black Caucus.

“What I do know: If I don’t get this and I don’t get this, and we don’t move for something, then we get nothing,” said Representative Joyce Beatty of Ohio, the chairwoman of the caucus. “And everybody wants both of the bills to pass.”

As night fell on Friday, however, it was unclear whether the gambit would succeed. Ms. Pelosi could be seen huddling with some of her top deputies on the House floor as she fielded phone calls and pored over what appeared to be a spreadsheet of how lawmakers planned to vote.

“The goal posts moved rather dramatically, so we’re trying to find a way that we can get them back where they need to be and get to yes,” said Representative Jared Huffman, Democrat of California, a progressive. “There are other concerns that have to be addressed, there are assurances that have to be sufficient” from the moderates, he added, before liberals allow the infrastructure bill to pass.

But for some progressives, no amount of assurances were sufficient. Representative Cori Bush, Democrat of Missouri, said she was a “hard no” on passing the infrastructure bill without also passing the social policy plan.

“There is no phone call I could get or offer that could change my mind,” she said, adding that progressives’ trust in their centrist colleagues was “hanging by a thread.”

Catie Edmondson, Luke Broadwater and Zolan Kanno-Youngs contributed reporting.