President Obama won the opening round of the 2013 fiscal fight with Republicans by pushing through a tax increase for the wealthiest Americans. But there are other fiscal debates looming that will decide the true winner in an ideological war that could define the president's second term.

The deal struck this week to avoid the so-called fiscal cliff largely delivered on Obama's campaign promise to force the rich to pay more, but it left issues like deep spending cuts and money-saving changes to Medicare and Social Security for the new Congress that convenes Thursday. Also waiting to be addressed is the nation's borrowing limit, which has to be extended by Congress before the federal government runs out of money and defaults on its obligations.

The White House said its victory on tax increases will give the president leverage in those looming debates. Obama is already trying to use his newfound momentum to pressure Congress on the debt ceiling, which he portrayed as "far worse than the impact of a fiscal cliff."

"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," Obama said.

But it won't be that simple for the president.

Republicans signed off on a cliff deal that included virtually no spending cuts in part because they thought they could get even deeper cuts if they tied their demands to a fight over the debt ceiling.

GOP congressional aides told The Washington Examiner that lawmakers held their noses and voted for a package they didn't like out of fear of being blamed if income taxes on all Americans went up. And Obama, they noted, has been robbed of his most effective rhetorical weapon: his claim that Republicans are protecting millionaires instead of the middle class.

"Obama may believe that he can talk about taxes again, but even many Democrats aren't going to accept that," said Douglas Holtz-Eakin, former director of the Congressional Budget Office. "It's impossible to tax your way out of this. He's going to have to deal with spending."

The debate over spending cuts could also help Republican leaders win back party conservatives angry over the GOP's support of a tax increase.

"There should be not a single vote for any deal to avoid the real fiscal cliff -- the debt ceiling increase -- without the passage of a Balanced Budget Amendment to the Constitution," said former Pennsylvania Sen. Rick Santorum, a recent Republican presidential contender. "When given the chance to work towards finding a solution that won't burden our children and grandchildren with trillions of new debt, [Democrats] said no."

Obama's victory lap before returning to his Hawaii vacation highlighted a more aggressive tone that has become commonplace since his re-election. Progressives repeatedly hammered Obama, especially in the last fight over the debt ceiling, for giving too much ground to Republicans.

Some said those days are long behind Obama.

"I think the president is in strong shape heading forward," said Democratic pollster Mark Mellman. "Republicans can't be seen as regularly holding the economy hostage. They can't reinforce that reputation."