In a letter released by the Treasury Department on Wednesday morning, Secretary Jack Lew said that on that date, “Treasury would have only approximately $30 billion to meet our country’s commitments.”

“This amount would be far short of net expenditures on certain days, which can be as high as $60 billion,” Lew wrote. “If we have insufficient cash on hand, it would be impossible for the United States of America to meet all of its obligations for the first time in our history.”

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This date is not a drastic departure from what Capitol Hill insiders estimated over the last few weeks. Both chambers saw mid October as the deadline for increasing the debt ceiling. House Republicans see this date as a sign that swift action is needed.

“This is another reminder that we need to work together – soon – on a bill that raises the debt limit and deals with causes of the debt by cutting Washington spending and increasing economic growth,” said Michael Steel, a spokesman for Boehner. “And it should remind President Obama that refusing to negotiate with Congress on solutions just isn’t an option.”

Lifting the nation’s borrowing limit is a legislative battle that has come to define Boehner’s House Republican majority. In 2011, Congress wrestled for too long with the legislation, and U.S. credit got downgraded.

“If Congress were to repeat that brinksmanship in 2013, it could inflict even greater harm on the economy,” Lew wrote. “And if the government should ultimately become unable to pay all of its bills, the result could be catastrophic.”

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Later this week, House Republicans will attempt to pass a bill to boost the debt ceiling for one year. That legislation will also include a one-year delay of the Affordable Care Act, alongside other Republican policies.

As Congress is working up a plan to fund the government past Oct. 1, Republicans have begun focusing on the debt ceiling as a place where they can force President Barack Obama to agree to a large-scale fiscal package. But in his letter, Lew sounded a skeptical tone.

“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,” he wrote. “Extending borrowing authority does not increase government spending; it simply allows the Treasury to pay for expenditures Congress has already approved. As such, I respectfully urge Congress to act immediately to meet its responsibility by extending the nation’s borrowing authority.”