Correction: An earlier version of this story misstated the name of the congressional committee that heard Geithner’s testimony. It also misstated the size of the U.S.’s current debt and how much more the Treasury can borrow. This version has been corrected.

The federal government will likely hit its borrowing limit before the end of the year, setting up another showdown over the federal debt immediately after the 2012 presidential election, according to Treasury Secretary Timothy F. Geithner.

In testimony to the Senate Budget Committee on Thursday, Geithner said he expects that the debt ceiling will be hit after Sept. 30, the end of the fiscal year, but before the beginning of 2013.

Under an agreement forged in the summer, the Treasury can borrow up to $16.4 trillion before returning to Congress for permission to borrow more. The debt currently stands at $15.4 trillion.

While some officials had hoped the borrowing authority would last through early 2013, that appears unlikely. Congress is close to extending a payroll tax cut through the end of this year without paying for it, requiring about $100 billion more in borrowing.

“I think even with agreement and prospect on the payroll tax, we still do not expect that [we will reach] the debt limit until quite late in the year, significantly after the end of the fiscal year but before the end of the calendar year,” Geithner said.

A fight over raising the debt limit may be one of three hugely consequential issues to be decided by Congress and the president immediately after the election. The other two are the expiration of the Bush-era tax cuts for the upper and middle class and automatic, deep spending cuts in the budgets of the Pentagon and domestic agencies set to begin next year.

Guessing when the country will hit the debt limit is an imprecise art. In addition, Congress has given the Treasury secretary a series of measures, such as using money in a special currency fund and postponing payments to civil pensions, to buy time if needed.

The odds of reaching the debt limit before the election are unknown, but Treasury officials have strongly suggested they’d invoke those extraordinary measures if that were to happen.