U.S. President Joe Biden and top congressional Republican Kevin McCarthy on Thursday appeared to be nearing a deal to cut spending and raise the government's $31.4 trillion debt ceiling, with little time to spare to head off the risk of default.

The deal would specify the total amount the government could spend on discretionary programs like housing and education. The two sides are now $70 billion apart on a total figure that would be well over $1 trillion.

The two sides met virtually on Thursday, the White House said. Representative Garret Graves, the top Republican negotiator, told reporters on Thursday evening that conversations would continue into the night.

Republican negotiators have backed off plans to increase military spending while cutting non-defense spending and instead backed a White House push to treat both budget items more equally.

Biden said they still disagreed over where the cuts should fall, noting that "I don't believe the whole burden should fall back to middle class and working-class Americans."

Graves told reporters that the White House is "refusing to negotiate on work requirements" for anti-poverty programs, which he called "crazy." He said disagreements over funding social security and Medicare versus work requirements remains an issue between the two sides.

House Speaker McCarthy told reporters Thursday evening that the two sides have not reached a deal.

It is unclear precisely how much time Congress has left to act. The Treasury Department was warned that it could be unable to cover all its obligations as soon as June 1, but on Thursday said it would sell $119 billion worth of debt that will come due on that date.

Any agreement will have to pass the Republican-controlled House of Representatives and the Democratic-controlled Senate. That could be tricky, as some right-wing Republicans and many liberal Democrats said they were upset by the prospect of compromise.

"I don't think everybody's going to be happy at the end of the day. That's not how the system works," McCarthy said.

The House adjourned on Thursday afternoon for a week-long break, and the Senate is not in session. Lawmakers have been told to be ready to come back to vote if a deal is reached.

As per reports, the deal would only set broad spending outlines, leaving lawmakers to fill in the blanks in the weeks and months to come and it would specify the total amount of military spending, which has been a key sticking point in the talks.

Biden has resisted Republican proposals to stiffen work requirements for anti-poverty programs and loosen oil and gas drilling rules, according to Democratic Representative Mark Takano.

Representative Kevin Hern, who leads the Republican Study Committee said that a deal was likely by Friday afternoon.

(With input from Reuters)