U.S. President Joe Biden and House Speaker Kevin McCarthy met again Monday for tense Oval Office talks on raising the government's borrowing limit - and, again, reached no agreement - as the U.S. government stares down a looming deadline for its first-ever default.

U.S. Treasury Secretary Janet Yellen, in a letter to congressional leaders Monday, said the government could default on its debt as early as June 1, and warned that even waiting until close to that time to reach an agreement 'can cause serious harm to business and consumer confidence, raise short-term borrowing costs for taxpayers and negatively impact the credit rating of the United States.'

On Tuesday, a Washington research group, the Bipartisan Policy Center, also warned of the possible financial peril the U.S. faces.

Debt Ceiling Explained: Why It's a Struggle in Washington and How the Impasse Could End

'Come early June, [the U.S.] Treasury will be skating on very thin ice that will only get thinner with each passing day,' Shai Akabas, executive director of the group's economic policy program, said in a statement. 'Of course, the problem with skating on thin ice is that sometimes you fall through.'

'The longer policymakers wait to address the debt limit, the more likely our economic fate will be determined by external actors,' Akabas said. 'Credit-rating agencies, Treasury investors, and global financial markets aren't going to wait around forever. Once things turn, the situation could deteriorate quickly and be hard to reverse, which would immediately and negatively impact American consumers and businesses.'

On Monday, as Biden and McCarthy sat down for another meeting, the president said failing to act could have major consequences.

'The American people would have a real kick in their economic well-being,' said Biden, who cut short an overseas trip to return to Washington for the debt negotiations. 'As a matter of fact, the rest of the world would, too.'

Biden and McCarthy have met three times in recent weeks but have yet to reach a deal on future government spending, even as they say they are making progress and that neither wants a government default.

'We don't have an agreement yet, but I did feel the discussion was productive in areas that we have differences of opinion,' McCarthy said Monday. He said the two negotiating teams would continue to talk via staffers.

Previous presidents and congressional leaders have reached deals to raise the country's debt limit 78 times in give-and-take negotiations in which neither side got everything on its wish list for the federal budget.

In the current debate, Republicans in the House have called for sharp government spending cuts, while the White House has countered with proposals to close tax loopholes and enact more limited spending reductions.

Republicans also want increased work requirements for able-bodied poor people receiving government assistance, but Democrats say that under such a proposal, several hundred thousand people could lose the benefits they now receive.

Republicans also are seeking cuts in funding for the country's tax-collection agency and asking the White House to accept provisions from their party's proposed immigration overhaul to reduce the number of migrants trying to enter the United States at the Mexican border.

Biden said in a statement after the talks, 'We reiterated once again that default is off the table and the only way to move forward is in good faith toward a bipartisan agreement.'

The president said he had done his part by offering ways to raise the country's $31.4 trillion borrowing limit so the U.S. government can keep paying its bills, such as interest on government bonds, stipends to U.S. pensioners, payments to health care providers and salaries for government employees and contractors.

But as Biden warned Monday, the tight balance of political power in Congress means that any deal needs to appeal to both Democratic and Republican lawmakers. He has previously called House Republicans' spending plan an 'extreme position.'

'We have to be in the position where we can sell it to our constituencies,' Biden said. 'We are pretty well divided in the House, almost down the middle. And it's not any different in the Senate. So, we've got to get something we can sell to both sides.'

Jeffrey Harris, a finance professor at American University in Washington, said, 'The uncertainty that the debt ceiling injects into the economy adds another element of risk to the tenuous economic conditions that we are already experiencing.'

'On top of the added burden of inflation and higher borrowing costs, consumer confidence is already near all-time lows. The possibility of a continuing U.S. impasse driving rates higher would compound current consumer issues and threatens to push the economy into a worse state,' he said.

Some information for this story came from The Associated Press, Agence France-Presse and Reuters.