WASHINGTON — With just five days left to make a deal, President Obama and members of the Senate were set to return to Washington on Thursday with no clear path out of their fiscal morass even as the Treasury Department warned that the government will soon be unable to pay its bills unless Congress acts.

Treasury Secretary Timothy F. Geithner, adding to the building tension over how to handle a year-end pileup of threatened tax increases and spending cuts, formally notified Congress on Wednesday that the government would hit its statutory borrowing limit on Monday, raising anew the threat of a federal default as the two parties remained in a standoff.

Mr. Geithner wrote that he would take “extraordinary measures” to keep the government afloat but said that with so much uncertainty over the shape of the tax code and future government spending he did not know how long the Treasury could shuffle accounts before the government could no longer pay its creditors.

For months, President Obama, members of Congress of both parties and top economists have warned that the nation’s fragile economy could be swept back into recession if the two parties did not come to a post-election compromise on January’s combination of tax increases and across-the-board spending cuts.