President vows not to negotiate on debt ceiling

After Congress' narrow dodge of the fiscal cliff, Washington isn't exactly breathing easy.

Major fiscal fights remain for the coming session and President Barack Obama has signaled his unwillingness to put Americans through another drawn-out battle over the nation's debt limit, which Congress will vote on this term.

"While I will negotiate over many things, 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 late Tuesday night after the fiscal cliff compromise.

The nation hit the debt ceiling limit on Monday.

Republicans have pushed back against raising the debt limit in past years, and this time around they're expected to use the fiscal cliff negotiations as leverage to press Democrats to compromise on spending cuts.

"I hope Republicans will fight as hard on the debt ceiling as Barack Obama did on tax rates," Sen. Lindsey Graham, R-S.C., said on Monday during an appearance on Fox News.

Congress will also be pushed in the coming session to address the deficit reduction and other fiscal measures the fiscal cliff deal failed to include.