WASHINGTON — Republicans stumbled on Thursday in their efforts to find agreement on a broad new proposal to lift the struggling economy, with Senate leaders and the Trump administration at odds over multiple provisions, including how to extend unemployment benefits and White House requests for spending unrelated to the pandemic.

Even after President Trump folded on one of his key demands, for a payroll tax cut, negotiations bogged down over details of the package, including how to reduce the amount of money that Americans are currently receiving as unemployment benefits.

Senate Republican leaders and administration officials were also discussing a push from the White House for money to rebuild the F.B.I. headquarters in Washington, long a preoccupation of the president, whose hotel is nearby on Pennsylvania Avenue, according to two people familiar with the talks.

Talks had reached consensus on several other fronts, including dropping Mr. Trump’s proposed payroll tax cut — an idea that had little support in either party on Capitol Hill — and providing additional loans to help small businesses endure the crisis.

The snag in negotiations delayed until Monday the rollout of what will effectively be Republicans’ opening bid in negotiations with congressional Democrats over a new stimulus package. Republicans have said they would support a package of around $1 trillion for this round of stimulus, while Democrats are demanding $3 trillion.

Thursday’s intramural squabbling among Republicans only increased the likelihood that Congress and Mr. Trump will fail to reach a deal before the supplemental benefit of $600 per week for unemployed Americans expires at month’s end. Failure to extend the supplemental benefit would result in sudden income losses for millions of people at a time when the economic recovery appears to have stagnated.

Lawmakers of both parties rejected the administration’s suggestion that Congress consider temporarily extending the enhanced unemployment insurance benefits and funding schools in a smaller bill while the larger stimulus package is hashed out.

“The administration has requested additional time to review the fine details, but we will be laying down this proposal early next week,” said Senator Mitch McConnell of Kentucky, the majority leader. The final elements, he said, would be revealed by Republicans on Monday after final negotiations with the administration.

“The sum of these efforts will be a strong, targeted piece of legislation aimed directly at the challenges we face right now,” he added.

The administration’s push for language to deal with a new F.B.I. headquarters was among multiple last-minute snags in the negotiations. Mr. Trump has previously taken steps to block a planned move by the bureau to the Washington suburbs and to turn its existing headquarters space over to a commercial developer, who could have installed a hotel to compete with the Trump International Hotel, which sits a block away.

Democrats criticized Mr. Trump this week after The New York Times reported that he had urged his ambassador to Britain to push officials there to select a golf club Mr. Trump owns in Scotland to host the British Open tournament.

Asked during his daily briefing whether the request for money for the headquarters, first reported by The Washington Post, was an issue in negotiations, Mr. Trump said there was “a lot of danger” in the building’s current condition.

“I’ve been encouraging them to build it, and you have a choice, you can renovate the existing building,” he said, adding that a new building could include a quarter-mile track on its roof. “I know they are talking about it, whether or not they put it in this bill or someplace else, but the F.B.I. needs a new building and we’ll get it done.”

Administration negotiators had proclaimed in the morning that an agreement was close at hand. Lobbyists circulated an outline of what was in it. Speaker Nancy Pelosi invited Senator Chuck Schumer of New York, the minority leader, to her weekly news conference, she said, in anticipation of offering a unified Democratic rebuttal to the Republican plan.

But Thursday ended without the release of legislative text. Lawmakers and aides sketched out the broad contours of a deal, with the persistent caveat that nothing was yet final.

Mr. McConnell said the package would include another round of direct payments to individuals, building on checks the Treasury Department sent to low- and middle-income households this spring.

The bill will also include a partial extension of enhanced unemployment benefits, at a lower level than laid-off workers are currently receiving, though there did not appear to be a final agreement between the administration and Senate Republicans on the details.

Treasury Secretary Steven Mnuchin and Mark Meadows, the White House chief of staff, told reporters after meeting with Mr. McConnell on Thursday morning that they would seek to limit the benefits to 70 percent of the wages workers had been receiving before they lost their jobs. For a typical worker, such a shift would mean $400 less per week in benefits — a drop from $600 in enhanced support now to about $200 under the proposal.

The exact mechanics of how that plan would work were still unfinished on Thursday.

Democrats said states would not have the time or the ability to engineer such a shift in benefit provisions before August, leaving unemployed workers struggling to make rent. They also said they would insist on renewing the $600 weekly benefit.

The day’s private lunch for Senate Republicans — a meal of alligator sausage, crab bisque and stuffed bell peppers furnished by Senator John Kennedy of Louisiana — featured a lively exchange of stories, but few details about why progress toward an agreement had slowed.

“Not a dang thing do I have for you — seriously,” Senator Lisa Murkowski, Republican of Alaska, said as she left the lunch on Thursday. “I was really hoping to be able to report to Alaskans what the contours of the Republican plan were. Now I won’t be able to, unless there’s something that comes out in the news.”

Senator Mike Rounds, Republican of South Dakota, told reporters that when lawmakers asked Mr. McConnell what progress had been made, he told them, “We’re working on it.”

Democrats accused their counterparts of wasting time and jeopardizing lives. “Now that Senate Republicans have finally woken up to the calamity in our country, they have been so divided, so disorganized, so unprepared that they have struggled to even draft a partisan proposal within their own conference,” Mr. Schumer said. “They can’t come together.”

Ms. Pelosi also rejected a suggestion from Mr. Mnuchin that Congress should take up a smaller package that prioritizes a few issues: the unemployment benefits, money for schools and liability protections for businesses and other institutions that are seeking to reopen.

“No, no, no — this is the package,” Ms. Pelosi said. “We cannot piecemeal this.”

Some details on the package’s contents became clear on Thursday, from summaries of the plan circulating on Capitol Hill and from comments by Mr. McConnell and some Republican committee leaders, like Senator Marco Rubio of Florida, who announced new plans to aid small businesses.

Mr. Rubio told reporters on Thursday that he expected the legislation to include at least $200 billion — in new funds and reallocated aid from previous packages — to assist small businesses.

That would include allowing certain hard-hit small businesses to apply for a second round of loans from the Paycheck Protection Program, which lawmakers created in March, and giving recipients more flexibility in how they could spend the money. The proposal would also restrict the number of eligible businesses, including by requiring evidence of steep revenue losses.

Mr. Rubio would also create an alternative loan program that would allow eligible businesses in low-income communities to receive long-term, low-interest loans that would cover their operating expenses through the expected duration of the crisis.

Despite the lack of final consensus on the Republican side, White House officials remained hopeful they could pull off an agreement in short order.

“Those deadlines, as you well know, on Capitol Hill always work magic in the 11th hour,” Mr. Meadows said.

Luke Broadwater, Nicholas Fandos and Carl Hulse contributed reporting.