A standoff between House Republicans and President Biden over raising the nation’s borrowing limit has administration officials debating what to do if the government runs out of cash to pay its bills, including one option that previous administrations had deemed unthinkable.

That option is effectively a constitutional challenge to the debt limit. Under the theory, the government would be required by the 14th Amendment to continue issuing new debt to pay bondholders, Social Security recipients, government employees and others, even if Congress fails to lift the limit before the so-called X-date.

That theory rests on the 14th Amendment clause stating that “the validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned.”

Some legal scholars contend that language overrides the statutory borrowing limit, which currently caps federal debt at $31.4 trillion and requires congressional approval to raise or lift.

Top economic and legal officials at the White House, the Treasury Department and the Justice Department have made that theory a subject of intense and unresolved debate in recent months, according to several people familiar with the discussions.

It is unclear whether President Biden would support such a move, which would have serious ramifications for the economy and almost undoubtedly elicit legal challenges from Republicans. Continuing to issue debt in that situation would avoid an immediate disruption in consumer demand by maintaining government payments, but borrowing costs are like to soar, at least temporarily.

Still, the debate is taking on new urgency as the United States inches closer to default. Treasury Secretary Janet L. Yellen warned on Monday that the government could run out of cash as soon as June 1 if the borrowing cap is not lifted.

Mr. Biden is set to meet with Speaker Kevin McCarthy of California at the White House on May 9 to discuss fiscal policy, along with other top congressional leaders from both parties. The president’s invitation was spurred by the accelerated warning of the arrival of the X-date.

But it remains unclear what type of compromise may be reached in time to avoid a default. House Republicans have refused to raise or suspend the debt ceiling unless Mr. Biden accepts spending cuts, fossil fuel supports and a repeal of Democratic climate policies, contained in a bill that narrowly cleared the chamber last week.

Mr. Biden has said Congress must raise the limit without conditions, though he has also said he is open to separate discussions about the nation’s fiscal path.

A White House spokesman declined to comment on Tuesday.

A group of legal scholars and some liberal activists have pushed the constitutional challenge to the borrowing limit for more than a decade. No previous administration has taken it up. Lawyers at the White House and the Justice and Treasury Departments have never issued formal opinions on the question. And legal scholars disagree about the constitutionality of such a move.

“The Constitution’s text bars the federal government from defaulting on the debt — even a little, even for a short while,” Garrett Epps, a constitutional scholar at the University of Oregon’s law school, wrote in November. “There’s a case to be made that if Congress decides to default on the debt, the president has the power and the obligation to pay it without congressional permission, even if that requires borrowing more money to do so.”

Other legal scholars say the limit is constitutional. “The statute is a necessary component of Congress’s power to borrow and has proved capable of serving as a useful catalyst for budgetary reform aimed at debt reduction,” Anita S. Krishnakumar, a Georgetown University law professor, wrote in a 2005 law review article.

The president has repeatedly said it is the job of Congress to raise the limit in order to avoid an economically catastrophic default.

Top officials, including Ms. Yellen and the White House press secretary, Karine Jean-Pierre, have sidestepped questions about whether they believe the Constitution would compel the government to continue borrowing to pay its bills after the X-date.

ABC News asked Ms. Yellen amid a debt-ceiling standoff in 2021 if she would invoke the 14th Amendment to resolve it.

“It’s Congress’s responsibility to show that they have the determination to pay the bills that the government amasses,” she said. “We shouldn’t be in a position where we need to consider whether or not the 14th Amendment applies. That’s a disastrous situation that the country shouldn’t be in.”

The government reached the borrowing limit on Jan. 19, but Treasury officials are able to deploy what are known as extraordinary measures to continue paying bills on time. The measures, which are essentially accounting maneuvers, are set to run out sometime in the next few months, possibly as soon as June 1. The government would default on its debt if Treasury stopped paying all bills. Economists have warned that could lead to financial crisis and recession.

Progressive groups have encouraged Mr. Biden to take actions meant to circumvent Congress on the debt limit and continue uninterrupted spending, like minting a $1 trillion coin to deposit with the Federal Reserve. Internally, administration officials have rejected most of them. Publicly, Biden aides have said the only way to avert a crisis is for Congress to act.

“I know you probably get tired of me saying this from here over and over again, but it is true,” Ms. Jean-Pierre said on Thursday, after referring a question about the 14th Amendment to the Treasury Department. “It is their constitutional duty to get this done.”

But inside the administration, it remains an open question what Treasury would do if Congress does not raise the limit in time — because, many officials say, the law is unclear and so is the Constitution, which gives Congress the power to tax and spend.

Officials who support invoking the 14th Amendment and continuing to issue new debt contend the government would be exposed to lawsuits either way. If it fails to continue paying its bills after the X-date, it could be sued by anyone who is not paid on time in the event of a default.

Other officials have argued that the statutory borrowing limit is binding, and that an attempt to ignore it would draw an immediate legal challenge that would most likely rise quickly to the Supreme Court.

There is a broad consensus on both sides of the debate that the move risks roiling financial markets. It is likely to cause a surge in short-term borrowing costs because investors would demand a premium to buy debt that could be invalidated by a court.

The Moody’s Analytics economist Mark Zandi modeled such a situation this year and found it would create short-term economic damage but long-term gains if courts upheld the constitutional interpretation — by removing the threat of future brinkmanship over the limit.

“The extraordinary uncertainty created by the constitutional crisis leads to a sell-off in financial markets until the Supreme Court rules,” Mr. Zandi wrote in March. Economic growth and job creation would be dampened briefly, he added, “but the economy avoids a recession and quickly rebounds.”

Obama administration officials briefly considered — and quickly discarded — the constitutional theory when Republicans refused to raise the limit in 2011 unless the president agreed to spending cuts. Treasury lawyers never issued a formal opinion on the question, and they have not yet this year, department officials said this week.

But in a letter to the editor of The New York Times in 2011, George W. Madison, who was Treasury’s general counsel at the time, suggested that department officials did not subscribe to the theory. He was directly challenging an assertion by the constitutional law professor Laurence H. Tribe, who wrote in an opinion essay in The Times that Treasury Secretary Timothy F. Geithner had pushed to embrace the 14th Amendment interpretation, which Mr. Tribe opposed.

“Like every previous secretary of the Treasury who has confronted the question,” Mr. Madison wrote, “Secretary Geithner has always viewed the debt limit as a binding legal constraint that can only be raised by Congress.”

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