Washington — The Treasury will only have $30 billion of cash on hand by mid-October, putting the United States on the precipice of an unprecedented default, the department said on Wednesday.

The warning puts additional pressure on a hamstrung Congress, which is already struggling to prevent the federal government from shutting down over a budget impasse on Oct. 1.

In a letter to Speaker John A. Boehner of Ohio, Treasury Secretary Jacob J. Lew warned that a single day's net expenditures can be as high as $60 billion. On any given day after that mid-October deadline, money going out might overwhelm money coming in plus cash on hand.

That means that until Congress lifts its statutory debt ceiling, the Treasury could miss or be forced to delay paying some of its bills. Such an event would be unprecedented, and financial analysts anticipate a violent market reaction that might raise federal borrowing costs, slow the recovery and destabilize markets around the world.

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.

"The United States should never have to choose, for example, whether to pay Social Security to seniors, pay benefits to our veterans, or make payments to state and local jurisdictions and health care providers under Medicare and Medicaid," Mr. Lew wrote.

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

But Republicans are currently debating what legislation to tie to raising the debt ceiling, such as defunding the Affordable Care Act or new spending cuts. That has set up a second showdown over budget and financial issues.

"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. "Extending borrowing authority does not increase government spending; it simply allows the Treasury to pay for expenditures Congress has already approved."

The potential costs from a debt-ceiling default might dwarf the costs associated with a government shutdown. The Bipartisan Policy Center, a Washington research group, has estimated that market concern over the potential of a default in 2011 cost nearly $19 billion over 10 years.

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.

In the letter, Mr. Lew set Oct. 17 as the effective deadline for Congressional action: after that date, the country would be at severe risk of missing or defaulting on some of its payments every day going forward.

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.