WASHINGTON — Unless Congress raises the debt ceiling, the Treasury Department said on Monday that it expected to lose the ability to pay all of the government’s bills in mid-October.

That means a recalcitrant Congress will face two major budget deadlines only two weeks apart, since the stopgap “continuing resolution” that finances the federal government runs out at the end of September.

Members of Congress are sharply divided over what to include in measures financing the government and raising the debt ceiling.

Some Republican lawmakers have said they want to see an increase in the debt limit paired with other measures to decrease the deficit. “We’re not going to raise the debt ceiling without real cuts in spending,” Speaker John A. Boehner of Ohio told reporters last month.