With the president refusing to negotiate over the essential increase and Republicans saying he must, reporters pressed Mr. Obama about whether he is considering some executive action to sidestep Congress and raise the debt ceiling — as Democratic leaders have urged. But Mr. Obama declined to answer directly, and his administration has ruled out proposals to either invoke authority under the 14th Amendment or mint a platinum coin as a sort of collateral for more debt.

The debt issue dominated the news conference, and later the Treasury secretary, Timothy F. Geithner, added to the pressure by writing to Congressional leaders that the department still expects to hit the limit between mid-February and early March.

“Treasury would be left to fund the government solely with the cash we have on hand on any given day,” he said, forcing it to choose among creditors, federal contractors, veterans, Social Security and Medicare beneficiaries and the many other claimants to federal dollars. Some Republicans support temporarily making choices among claimants, but the administration and some financial analysts say that approach would be unworkable and amount to the nation’s first default on its obligations.

Separately, Mr. Geithner and Gene Sperling, director of the White House National Economic Council, held a conference call with corporate executives, many of whom have expressed concern the threat of default could damage the economy. The administration is hoping that business leaders can persuade Republicans to avoid confrontation over the debt limit, but party leaders were undeterred.

The Federal Reserve chairman, Ben S. Bernanke, also called on Congress to increase the debt ceiling to cover bills that it has already incurred. “The right way to deal with this problem is for Congress to do what it is supposed to do and what it needs to do,” Mr. Bernanke, a Republican appointed by President George W. Bush and later reappointed by Mr. Obama, said in a speech at the University of Michigan.