By David Morgan and Jarrett Renshaw

WASHINGTON Democratic President Joe Biden and top congressional Republican Kevin McCarthy will sit down on Tuesday to try to make progress on a deal to raise the U.S. government's $31.4 trillion debt ceiling and avert an economically catastrophic default.

They have little time to reach a deal. The U.S. Treasury Department on Monday reiterated its warning that it could run short of money to pay all its bills as soon as June 1, which would trigger a default that economists say would be likely to spark a sharp economic downturn.

Republicans, who control the House of Representatives by a 222-213 majority, have for months demanded that any increase in the government's self-imposed borrowing cap be linked to spending cuts. In the past week, staffs for both sides have discussed a range of issues, including spending caps and changes to energy permitting in exchange for votes to lift the limit, according to people briefed on the talks.

White House officials have described the talks as constructive, but McCarthy on Monday warned that he believed little progress had been made.

"If you look at the timeline to pass something in the House and pass something in the Senate, you've got to have something done by this weekend," McCarthy told reporters. "And we are nowhere near any of that."

Biden is due to leave town on Wednesday to attend a meeting of the Group of Seven rich nations in Japan, while the House is currently scheduled to leave Washington for a week-long recess after Thursday's session.

Democrats including Senate Majority Leader Chuck Schumer, who is also expected to attend Tuesday's White House meeting, said that talks were proceeding in a "serious way."

He criticized Republicans for blocking a debt ceiling hike after helping to raise it three times under Biden's Republican predecessor, Donald Trump.

"Default must be taken off the table," Schumer said in a Monday speech on the Senate floor. "No one should play with it. No one should flirt with it. No one should hold it hostage and say unless you do this, we're going to default, because the consequences of default are just awful."

A similar 2011 standoff led to a historic downgrade of the United States' credit rating, which sparked a selloff in stocks and pushed its borrowing costs higher.

The current standoff has rattled investors, sending the cost of insuring exposure to U.S. government debt to record highs, and a Reuters/Ipsos poll completed on Monday found that three-quarters of Americans fear that a default would take a heavy toll on families like theirs.

'TOO MANY COOKS'

Some observers have raised concerns that the five-party talks -- featuring Biden, McCarthy, Schumer, top Senate Republican Mitch McConnell and top House Democrat Hakeem Jeffries -- are too unwieldy to make progress.

No. 2 Senate Republican John Thune told reporters that the talks appear to have "too many cooks."

"As we've said all along, it is Biden and McCarthy," Thune said. "So, whoever can actually speak on behalf of the president needs to get in the room, and get McCarthy's best people in there, and get it done."

Adding to the challenge of striking a deal, McCarthy agreed to a change in House rules that allows for just one member to call for his ouster as speaker, which gives greater power to hardliners, including the roughly three dozen members of the House Freedom Caucus.

(Reporting by David Morgan and Jarrett Renshaw, additional reporting by Jeff Mason, Richard Cowan and Moira Warburton; Editing by Scott Malone and Rosalba O'Brien)