Treasury Secretary Janet L. Yellen said on Monday that the United States could run out of money to pay its bills by June 1 if Congress does not raise or suspend the debt limit, putting pressure on President Biden and lawmakers to reach a swift agreement to avoid defaulting on the nation’s debt.

The more precise warning over when the United States could hit the so-called X-date dramatically reduces the projected amount of time lawmakers have to reach a deal before the government runs out of money to pay all of its bills on time.

The new timeline could accelerate negotiations between the House, Senate and Mr. Biden over government spending — a high-stakes standoff between the president and the House Republicans who have refused to raise the limit without deep spending cuts attached.

In response to Ms. Yellen’s new timeline, Mr. Biden on Monday called the top four leaders in Congress to ask for a meeting on May 9 to discuss fiscal issues. The president reached out to Speaker Kevin McCarthy and Representative Hakeem Jeffries of New York, the minority leader, along with Senator Chuck Schumer of New York, the majority leader, and Senator Mitch McConnell of Kentucky, the minority leader.

Economists have warned that failure to raise the debt limit, which caps the total amount of money the United States can borrow, threatens to rock financial markets and throw the global economy into a financial crisis.

Because the United States runs a budget deficit — meaning it spends more money than it takes in — it must borrow huge sums of money to pay its bills. In addition to paying Social Security benefits, along with salaries for the military and government workers, the United States is also required to make interest and other payments to the bondholders who own its debt.

The Treasury Department had previously projected that it could run out of cash sometime in early June, but the new estimate raises the alarming prospect that the United States could be unable to make some payments, including to bondholders, in a matter of weeks.

“Given the current projections, it is imperative that Congress act as soon as possible to increase or suspend the debt limit in a way that provides longer-term certainty that the government will continue to make its payments,” Ms. Yellen said in a letter to Congress.

The Congressional Budget Office also warned on Monday that time was running out more quickly than previously thought. The nonpartisan budget office said tax receipts from income payments that were processed in April were smaller than it had anticipated and that future tax payments were unlikely to have much impact.

“That, in combination with less-than-expected receipts through April, means that the Treasury’s extraordinary measures will be exhausted sooner than we previously projected,” Phillip Swagel, the C.B.O. director, wrote in an analysis posted on the agency’s website.

White House officials had not expected the date of possible default to arrive so soon, and the accelerated timetable could scramble the president’s approach to the potential crisis.

Mr. Biden has continued to insist he will not negotiate directly over the limit, saying Congress must raise the cap without conditions. The newly compressed calendar leaves little time for the president and congressional leaders to find agreement on raising the limit. Mr. McCarthy is traveling in the Middle East this week. Later this month, Mr. Biden is scheduled to attend the Group of 7 nations leaders’ summit in Japan, then travel on to Australia for a summit with the leaders of Japan, India and Australia.

House Republicans passed legislation in April that would raise the debt limit in exchange for deep spending cuts and roll back recent climate legislation that Democrats passed along party lines. Mr. Biden has blasted that bill, saying it would hurt working families while benefiting the oil and gas industry, and he has accused Republicans of putting America’s economy on the line.

On Monday, the president called on Republicans “to make sure the threat by the Speaker of the House to default on the national debt is off the table.”

“For over 200 years, America has never, ever, ever failed to pay its debt. To put in the capital — in colloquial terms, America is not a deadbeat nation. We have never, ever failed to meet the debt,” Mr. Biden said.

Republican Senators reacted to the news on Monday by emphasizing the onus was now on Mr. Biden to negotiate to avoid economic calamity.

“It is very scary,” Senator Joni Ernst of Iowa and a member of Republican leadership said of the looming crisis. “President Biden needs to step it up and get to the table. Kevin McCarthy and the folks in the house, they did their part.”

Some expressed optimism that the approaching deadline would force action.

“Washington’s at its best when it has a deadline to respond to,” Senator Thom Tillis, Republican of North Carolina, said.

Mr. Schumer and Mr. Jeffries urged Republicans to lift the limit immediately with no strings attached. “We do not have the luxury of waiting until June 1 to come together, pass a clean bill to avoid a default and prevent catastrophic consequences for our economy and millions of American families,” the lawmakers wrote in a joint statement on Monday.

While there is bipartisan agreement that the nation needs to find a way to reduce the gap between when it spends and what it collects, even the most ardent supporters of fiscal reform say the debt limit must be raised.

“We need to raise the debt limit as soon as possible, without drama and without serious risk of default,” said Maya MacGuineas, the president of the Committee for a Responsible Federal Budget. “To threaten default or drag one’s feet is the height of irresponsibility. Lawmakers need to commence serious discussions immediately.”

The possibility of a default by June 1 could compel lawmakers to agree to a short-term increase or suspension of the debt limit to provide more time for negotiations. But even that temporary salve is far from assured given competing factions within the Republican Party.

The United States technically hit its $31.4 trillion debt limit in January, forcing the Treasury Department to employ accounting maneuvers known as extraordinary measures to allow the government to keep paying its bills, including payments to bondholders who own government debt. Ms. Yellen said at the time that her powers to delay a default — in which the United States fails to make its payments on time — could be exhausted by early June. She cautioned, however, that the estimate came with considerable uncertainty.

Tax receipts depend on a complicated array of factors such as the jobless rate, wages and whether taxpayers submit their returns on time. On Monday, the Treasury secretary underscored the challenges of predicting the default date, noting that the new estimate was based on currently available data that is inherently variable, such as tax payments from individuals.

“The actual date that Treasury exhausts extraordinary measures could be a number of weeks later than these estimates,” Ms. Yellen said.

A Treasury Department official said that, as of April 30, the government had a cash balance of about $300 billion. Ms. Yellen’s ability to delay a default will depend in part on how much tax revenue comes into the federal government this spring.

Payments for the 2022 tax year are still arriving. Goldman Sachs economists projected last week that by the second week of June, the Treasury Department could have about $60 billion of cash remaining, which would allow the government to keep making its payments until late July.

Some budget analysts have suggested that winter storms could complicate the Treasury Department’s ability to delay a default. Severe storms, flooding and mudslides in California, Alabama and Georgia this year prompted the Internal Revenue Service to push the April 18 filing deadline to October for dozens of counties.

The I.R.S. also gave those affected areas more time to make contributions to retirement and health savings accounts, potentially affecting their taxable income.

Ms. Yellen has already been taking steps to ensure that the federal government has sufficient cash on hand.

Earlier this year, she announced that she would redeem some existing investments and suspend new investments in the Civil Service Retirement and Disability Fund and the Postal Service Retiree Health Benefits Fund.

Ms. Yellen said on Monday that the Treasury Department was suspending the issuance of State and Local Government Series Treasury securities to help manage the risks associated with the debt limit. She lamented that the move would deprive state and local governments of an important tool to manage their finances.

Brinkmanship over the debt limit has revived debates over how far the executive branch can go to avoid a default. Ms. Yellen, however, has dismissed the notion that she could prioritize certain payments or mint a platinum coin worth $1 trillion to ensure that the United States remains solvent.

Although markets have broadly remained calm about the prospect of a default, there are some signs that investors are becoming nervous.

They have sold government bonds that mature in three months — around the time policymakers have said the United States could run out of cash — and snapped up bonds with just one month until they are repaid.

The cost of insuring existing bond holdings against the possibility that the United States will default on its debts has also risen sharply. Still, some analysts say the market reaction would need to be much more pronounced to force a fast deal.

In a separate report issued by the Treasury Department on Monday about the risks facing the economy, Eric Van Nostrand, the acting assistant secretary for economic policy, laid out the dire consequences of failing to raise the debt limit.

“A default by the U.S. government — including the failure to pay any of the United States’ obligations — would be an economic catastrophe, sparking a global downturn of unknown but substantial severity,” Mr. Van Nostrand said.

The New York Times News Service