WASHINGTON — The Treasury has handed Congress an urgent deadline: Oct. 17.

On that day, unless Congress were to raise the debt ceiling, the Treasury would have only $30 billion cash on hand, putting the United States on the precipice of an unprecedented default, the department said on Wednesday.

That warning – and the threat of a financial crisis – have become entangled in the budget and financial negotiations on Capitol Hill, where legislators are already engaged in a partisan battle that has led to a budget impasse that could shut down the federal government on Oct. 1.

Separately on Wednesday, the nonpartisan Congressional Budget Office estimated that the Treasury would exhaust all its extraordinary measures and run out of free cash between Oct. 22 and Nov. 1.

In a letter to Speaker John A. Boehner of Ohio, Treasury Secretary Jacob J. Lew urged Congress to raise the debt ceiling in a clean bill and avoid any question of default.

“The president remains willing to negotiate over the future direction of fiscal policy, but he will not negotiate over whether the United States will pay its bills for past commitments,” Mr. Lew said.

But some Republicans are planning on tying other measures to a debt ceiling vote, perhaps cuts to entitlement programs and a delay in the individual mandate in the health care law.

In response to the Treasury letter, the Republicans on the Senate Finance Committee demanded that the White House open up for broader fiscal negotiations, and also detail how much of a debt-limit increase it wanted.

“For decades, Congress and various administrations have used the debt limit as an opportunity to confront budgetary, fiscal, and other matters,” they wrote. “This debt limit increase should be viewed similarly – as an opportunity to bring lasting reforms and debt reduction to our nation.”

Mr. Lew warned in his letter that a single day’s net expenditures could be as high as $60 billion. After that mid-October deadline, money going out might overwhelm money coming in plus cash on hand. The Treasury could miss or be forced to delay paying some of its bills.

Such an event would be unprecedented, and many financial analysts fear a possible violent market reaction with global ramifications.

Privately, economic officials have worried that the numerous near-brushes with a debt ceiling or other budgetary crisis in the last few years have inured the markets, with investors expecting Washington to wait until the last minute before acting.

If that expectation were to prove wrong, though, the effects are unknowable – and might be severe. “Any delay in raising the debt ceiling would have dire economic consequences,” said Mark Zandi of Moody’s Analytics, testifying on Capitol Hill this week. “Consumer, business and investor confidence would be hit hard, putting stock, bond and other financial markets into turmoil.”

In the event of a default, the United States’ borrowing costs would probably rise and continue at somewhat higher levels even after the Treasury Department returned to new issuance on the bond market, causing a direct hit to taxpayers. But financial analysts are more immediately worried about the potential for wide market gyrations as investors reassessed their pricing of trillions of dollars of debt products tied to Treasury rates and sought safety in new markets or instruments.

The costs from a debt-ceiling default would almost certainly dwarf the costs associated with a government shutdown, which most experts say would be relatively small if it did not continue for an extended period of time. The Bipartisan Policy Center, a Washington research group, estimated that market concern over the potential of a default in 2011 cost nearly $19 billion over 10 years, and that occurred even though the government avoided a default at the last minute.

The House recently passed legislation that would order Treasury to prioritize payments to bondholders — an action meant to soothe the markets in the event of a debt-ceiling crisis. But the Obama administration has rejected that idea and refused to negotiate over the debt limit more broadly.

“There is no way of knowing the damage any prioritization plan would have on our economy and financial markets,” Mr. Lew wrote. “It would represent an irresponsible retreat from a core American value: We are a nation that honors all of its commitments.”

The United States hit its statutory borrowing limit of about $16.7 trillion on May 19, meaning that Treasury could no longer issue new debt to pay the government’s bills. With the government running in the red, the Treasury has used a series of “extraordinary measures” to free up about $300 billion in cash. But those measures buy it only so much time.

The Treasury makes more than 80 million individual payments a month. After exhausting its extraordinary measures, it would miss about 30 percent of those payments until Congress raised the ceiling again.

According to the Bipartisan Policy Center, the Treasury is facing a $12 billion Social Security payment on Oct. 23 and a $6 billion interest payment on the public debt on Oct. 31. On Nov. 1 alone, it needs to spend $18 billion on Medicare, $25 billion on Social Security, $12 billion on military pay and veterans benefits and $3 billion on the Supplemental Security Income program.

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