Treasury Secretary Yellen said Sunday that there are “no good options” for the United States to avoid an economic “calamity” if Congress fails to raise the nation’s borrowing limit of $31.381 trillion in the coming weeks. She did not rule out President Biden bypassing lawmakers and acting on his own to try to avert a federal default.

Her comments added even more urgency to a high-stakes meeting Tuesday between Mr. Biden and congressional leaders from both parties.

Democrats and Republicans are at loggerheads over whether the debt limit should even be the subject of negotiation. GOP lawmakers, led by Speaker McCarthy, are demanding spending cuts in return for raising the borrowing limit, while Mr. Biden has said the threat of default shouldn’t be used as leverage in budget talks.

Ms. Yellen, interviewed on ABC’s “This Week,” painted a dire picture of what might happen if the borrowing limit is not increased before the Treasury Department runs out of what it calls “extraordinary measures” to operate under the current cap. That time, she said, is expected to come in early June, perhaps as soon as June 1.

“Whether it’s defaulting on interest payments that are due on the debt or payments for Social Security recipients or to Medicare providers, we would simply not have enough cash to meet all of our obligations,” she said. “And it’s widely agreed that financial and economic chaos would ensue.”

An increase in the debt limit would not authorize new federal spending. It would only allow borrowing to pay for what Congress has already approved.

Mr. Biden’s White House meeting with Mr. McCarthy, House Minority Leader Hakeem Jeffries, and Senators Schumer and McConnell, will be the first substantive talks between Messrs. Biden and McCarthy in months.

House Republicans on April 26 passed a bill that would raise the debt limit but impose significant federal spending cuts. But those cuts are unlikely to win the support of all Republicans in the Democratic-controlled Senate, and Mr. Biden has said he will only negotiate about government spending once Congress takes the risk of default off the table.

Senator Lee said Sunday that there are 45 Republicans in his corner willing to prevent Democrats from passing any sort of debt ceiling increase without spending reforms. Speaking on Fox News’ “Sunday Morning Futures,” the Utah senator said the number is more than enough to overcome the Senate’s filibuster rules.  

“As Kevin McCarthy, as Speaker of the House, meets with the White House, it’s imperative that he arrives with a position of negotiating power,” Mr. Lee said. “And to that end, we’ve got not only the Republican conference in the Senate backing what the Republicans in the House passed the week before last, we’ve also got a solid bloc of Republicans, more than enough, to block any sort of so-called ‘clean’ debt ceiling bill from going forward, anything that raises the debt ceiling without substantive spending and budgetary reforms.”

Senator Sinema, the independent who left the Democratic Party in December, encouraged Messrs. Biden and McCarthy to meet each other half way.

“There’s not going to be just a simple clean debt limit — the votes don’t exist for that,” she told CBS’s “Face the Nation.” “So the sooner these two guys get in the room and listen to what the other one needs, the more likely they are to solve this challenge and protect the full faith and credit of the United States of America.”

Ms. Yellen was asked on ABC whether Mr. Biden could bypass Congress by citing the Constitution’s 14th Amendment that the “validity” of American debt “shall not be questioned.” Ms. Yellen did not answer definitively, but said it should not be considered a valid solution.

“We should not get to the point where we need to consider whether the president can go on issuing debt. This would be a constitutional crisis,” she said.

“What to do if Congress fails to meet its responsibility? There are simply no good options,” she added.

Senator Lankford, an Oklahoma Republican, agreed about the risks of invoking the 14th Amendment. He told ABC that the Constitution is “very clear that spending — all those details around spending and money actually has to come through Congress.”

The 14th Amendment question was studied by Obama administration lawyers during the 2011 debt limit showdown, which informed Mr. Biden’s refusal to negotiate now with Republicans on raising the debt limit. At the time, Justice Department lawyers said they did not believe the president had the unilateral power to issue new debt.

Mr. Biden, in an interview with MSNBC on Friday, was asked about the 14th Amendment proposal, and replied, “I’ve not gotten there yet.”