But White House spokesman Jay Carney said that the US government had borrowing authority right up until "the end of the day" on Thursday.
"Beyond that, if there's not a resolution to this and the debt ceiling isn't lifted, then we have a cash-on-hand situation when it comes to meeting our obligations," Carney said.
Both chambers of Congress were expected to vote later on Wednesday on a deal brokered by Senate leaders to re-open the US government and extend America's borrowing authority until February 7 next year.
But given the often complicated and sluggish congressional procedures the timing could yet slip.
Carney's remarks, which were more specific than comments from the Obama administration in recent days, may be seen as a signal to markets that bureaucratic hitches will not disturb an apparent easing of the crisis.