WASHINGTON — Nearing a self-imposed deadline for a bipartisan infrastructure deal, President Biden met again on Wednesday with the lead Republican negotiator to try to resolve major differences over the size, structure and financing of an expansive public-works plan.

The roughly hourlong meeting in the Oval Office between Mr. Biden and Senator Shelley Moore Capito, Republican of West Virginia, did not end with any public breakthroughs, but they agreed to continue their discussions on Friday. The two were pressing to find a compromise before Congress returns next week, when Democratic leaders and administration officials have suggested they want to see clear movement toward a bipartisan deal, or they may begin pursuing their own plan without Republicans.

The latest talks came days after Ms. Capito and other Republicans proposed an overall $928 billion infrastructure package that would include about $257 billion in new funding for roads, bridges and other physical projects, compared with Mr. Biden’s latest plan for $1.7 trillion in new spending. Republicans have said that the president’s version is far too large and rejected his approach of raising taxes on corporations and wealthy individuals to pay for it; the White House has called the G.O.P. plan far too limited and ruled out the idea of using unspent coronavirus relief funds and increased user fees for drivers to finance it.

White House officials would not divulge details of the meeting on Wednesday. But it came at a critical time, as Mr. Biden’s team and Democrats on Capitol Hill are assessing whether a bipartisan deal is possible and how long to spend pursuing one before moving ahead to try to muscle through legislation on their own.

“Patience is not unending, and he wants to make progress,” Jen Psaki, the White House press secretary, said of the president before the meeting. She described it as “more of a discussion” rather than an exchange of documents or firm details.

A White House statement after the meeting characterized it as “constructive and frank” but gave no further details.

A spokeswoman for Ms. Capito said she was “encouraged that negotiations had continued” and suggested that the senator had made the case to Mr. Biden that a compromise was possible. Ms. Capito, the spokeswoman said, had “stressed the progress that the Senate has already made” by advancing bipartisan water projects and surface transportation bills through committee this year.

After rushing the $1.9 trillion pandemic relief package into law with only Democratic votes, the White House and congressional leaders face a far more difficult path for Mr. Biden’s ambitions to spend trillions of dollars to shore up the nation’s public works system, address racial and gender inequities in the work force, and provide for child and home care.

Senator Mitch McConnell of Kentucky, the minority leader, said at an event in his home state that he remained hopeful “that we can actually reach a bipartisan agreement on infrastructure.” But with many Republicans opposed to key elements of the White House plan, progressive Democrats and activists are urging leaders to abandon the effort to court G.O.P. support.

Under normal Senate procedures, 10 Republicans would have to break ranks and join Democrats in overcoming a filibuster of an infrastructure plan. But Democrats are weighing use of the fast-track budget reconciliation process, as they did with the stimulus law, to push the proposal through on a simple majority vote.

Some moderate Democrats, including Senator Joe Manchin III of West Virginia, have warned against rushing to abandon the bipartisan talks and are quietly working with Republicans on alternatives.

Mr. Biden and his top aides have insisted that they believe a bipartisan accord is feasible. But they have also been assessing their options for moving forward without one, which appeared to narrow in recent days with new guidance from the Senate’s top rules enforcer.

While the Senate parliamentarian, Elizabeth MacDonough, had previously indicated that they could move another reconciliation package quickly using the same budget blueprint that carried the pandemic aid bill, she has since advised them on additional constraints for doing so.

Ms. MacDonough’s memo, issued on Friday and reported earlier by Punchbowl News, warned that repeatedly using the same budget plan in a bid to circumvent the 60-vote filibuster threshold could harm the institution of the Senate.

Should Democrats try to do so, she added, the revised budget resolution would have to go through the Budget Committee, according to three people familiar with the guidance, who disclosed details on the condition of anonymity. That would be a particularly thorny process in the evenly divided Senate, according to one of the people, and it would consume considerable time.

Ms. MacDonough, according to two of the people, also suggested that Democrats would have to provide a legitimate reason — most likely tied to economic conditions — for reopening a budget blueprint. It is unclear how severe the circumstances would need to be or how Democrats would need to justify the maneuver.

The office of Senator Chuck Schumer of New York, the majority leader, announced this year that Ms. MacDonough had said that using the reconciliation tool a second time this fiscal year was possible. A spokesman called it a “key pathway” that would be available to Democrats while conceding that “some parameters still need to be worked out.”

Mr. Schumer’s office declined on Wednesday to publicly comment on the new guidance.