A similar stand-off two years ago triggered a downgrade of U.S. creditworthiness.

“We have seen a sizeable group of Republican lawmakers suggest they would not vote to pay the bills that Congress rang up - a fiasco that harmed a fragile economic recovery in 2011, and one we cannot afford to repeat,” said Obama.

The looming implementation of the Affordable Care Act, or Obamacare as it's commonly known, is further complicating the picture. The program compels Americans to purchase private health insurance, and provides subsidies for those of modest incomes. Some Republicans say they will not vote for any budget that contains funding for Obamacare. Obama will not sign any budget bill that does not.