Speaker John Boehner adamantly ruled out a House vote on a bill to boost the borrowing authority without concessions from President Barack Obama.
With no resolution in sight, US Treasury secretary Jack Lew warned Congress was "playing with fire" as he called on lawmakers to quickly pass legislation reopening the government and increasing the nation's £10.4 trillion debt limit.
The government shutdown precipitated by the budget brinkmanship has entered its second week with hundreds of thousands of federal employees at home with no pay, national parks closed and an array of government services on hold.
Mr Lew said Mr Obama has not changed his opposition to coupling a bill to reopen the government and raise the debt ceiling with Republican demands for changes to his three-year-old health care law and spending cuts.
Mr Boehner insisted that Mr Obama must negotiate if the President wants to end the shutdown and avert a default that could trigger a financial crisis and recession that would echo the events of 2008 or worse.
"We're not going to pass a clean debt limit increase," Mr Boehner, the top House Republican, said.
Democrats argue that their 200 members in the House of Representatives plus close to two dozen pragmatic Republicans would back a so-called "clean" bill.