Congressional leaders have failed to reach a deal on legislation to keep federal funding going past Friday, with Republicans insisting on adding right-wing policy dictates to the spending bills, pushing the government to the brink of a partial shutdown within days.

Senator Chuck Schumer, Democrat of New York and the majority leader, said on Sunday that despite “intense discussions” that were continuing among top lawmakers to break the impasse, Republican recalcitrance was raising the prospect of a “disruptive shutdown” at midnight on Friday.

“While we had hoped to have legislation ready this weekend that would give ample time for members to review the text, it is clear now that House Republicans need more time to sort themselves out,” Mr. Schumer said in a letter to Democratic senators. “With the uncertainty of how the House will pass the appropriations bills and avoid a shutdown this week, I ask all senators to keep their schedules flexible, so we can work to ensure a pointless and harmful lapse in funding doesn’t occur.”

With no sign of a breakthrough, President Biden summoned congressional leaders to the White House on Tuesday to discuss the spending legislation, as well as the $95 billion foreign aid package for Ukraine and Israel that the Senate passed earlier this month, which Speaker Mike Johnson has refused to take up.

But the more immediate task was to keep government spending from lapsing this week.

Three consecutive times over the last six months, Congress has relied on short-term, stopgap spending bills passed by a bipartisan coalition of lawmakers to keep government spending flowing, essentially punting on a longer-term agreement for several weeks at a time. Each time, the Republican speaker — first Kevin McCarthy, then Mr. Johnson — has promised hard-right lawmakers that they would try to win more spending cuts and conservative policy conditions on how federal money could be spent during the next round of negotiations.

Now, with patience wearing thin among ultraconservatives, pressure is mounting on Mr. Johnson, whose members want him to secure major cuts and policy changes that have no chance of enactment with Democrats in control of the Senate and White House. Lawmakers in the House, which has been out of session for the past week, are set to return to Washington on Wednesday, just two days before a deadline on Friday to fund military construction, agriculture, transportation and housing programs.

Funding for all other agencies, including the Pentagon, is set to lapse at midnight on March 8.

In a statement on Sunday, Mr. Johnson said he had been laboring to reach a compromise.

“Despite the counterproductive rhetoric in Leader Schumer’s letter, the House has worked nonstop, and is continuing to work in good faith, to reach agreement with the Senate on compromise government funding bills in advance of deadlines,” Mr. Johnson said, adding: “This is not a time for petty politics.”

Negotiators have continued to haggle over a series of partisan policy mandates that House Republicans had loaded into their spending bills, such as measures to restrict abortion access, that mainstream Republicans from competitive districts have refused to support.

Mr. Johnson in his statement on Sunday accused Senate Democrats of “attempting at this late stage to spend on priorities that are farther left than what their chamber agreed upon.”

Several House Republicans conceded weeks ago that they expected Mr. Johnson to have little success winning significant policy concessions. Mr. Johnson told Republicans on Friday during a conference call that they should not expect the inclusion of many of their major policy priorities, though he said he expected to secure a number of more minor victories, according to people familiar with the private discussion who described it on the condition of anonymity. Part of the reason they would have to settle for less, he explained, was that hard-right lawmakers had routinely blocked consideration of spending legislation, sapping the House’s leverage in talks with the Senate.

Instead, members of the ultraconservative Freedom Caucus have begun lobbying Mr. Johnson to instead pass a spending bill that would impose across-the-board cuts.

“If we are not going to secure significant policy changes or even keep spending below the caps adopted by bipartisan majorities less than one year ago, why would we proceed when we could instead pass a yearlong funding resolution that would save Americans $100 billion in year one?” they wrote in a letter to Mr. Johnson last week.

They were referring to a provision of the fiscal agreement made by Mr. McCarthy and Mr. Biden in May that would cut federal spending 1 percent across the board on April 30 if Congress could not reach a governmentwide spending deal before then.

But senators in both parties are determined to avoid that scenario because the cuts would particularly affect Pentagon spending.