WASHINGTON — With the resolution of the year-end fiscal crisis just hours old, the next political confrontation is already taking shape as this city braces for a fight in February over raising the nation’s borrowing limit. But it is a debate President Obama says he will have nothing more to do with.

Even as Republicans vow to leverage a needed increase in the federal debt limit to make headway on their demands for deep spending cuts, Mr. Obama — who reluctantly negotiated a deal like that 18 months ago — says he has no intention of ever getting pulled into another round of charged talks on the issue with Republicans on Capitol Hill.

“I will not have another debate with this Congress over whether or not they should pay the bills that they’ve already racked up through the laws that they passed,” the president said Tuesday night after he successfully pushed Republicans to allow tax increases on wealthy Americans. On Wednesday, he signed the legislation.

The president’s position is sure to appeal to his liberal allies, who fear another round of compromises by Mr. Obama. But it once again sets the stage for a nail-biting standoff that economists warn could lead to a damaging financial default and doubt from investors about the ability of the country to pay its obligations.