The president told congressional leaders Monday to return to the White House with a plan that could get both parties on board.
The clock is ticking to reach a deal by Aug. 2 to keep the country from defaulting on loans.
The two top Republicans in Congress put the blame on the president. Leader Mitch McConnell said a deal with Obama is "probably unattainable" and House Speaker John Boehner said the specter of default is "his problem."
McConnell maintained that White House offers to cut long-term spending amount to "smoke and mirrors" and directly challenged Obama's leadership. After years of discussions and months of negotiations," the Kentucky Republican said, "I have little question that as long as this president is in the Oval Office, a real solution is probably unattainable."
Obama has been pushing for $4 trillion in a 10-year deficit reduction proposal. But Boehner, after seeking to forge a deal of that magnitude, told the president that a smaller, $2 trillion to $2.4 trillion deal was more realistic.
Moody's Credit Agency has threatened to downgrade the U.S. credit rating before the government actually defaults. Analysts warn that Americans will see an immediate effect.
Democratic officials familiar with Obama's private talks with leaders of the House and Senate insist that Congress will not let the government go into default for the first time in American history.
The Associated Press contributed to this report.