President Obama said Friday that Congress will have to agree to make cuts in federal spending if it is also to reach a crucial deal in the coming months on raising the limit on how much the government can borrow.

“I think it’s absolutely right that it’s not going to happen without some spending cuts,” Obama said in an interview with the Associated Press.

Republicans have been saying for weeks that they would not raise the $14.3 trillion debt limit without deeper spending concessions by the president and congressional Democrats. The White House, however, has been saying that a vote to increase the debt limit must be separate from any other vote on spending.

The nation’s debt is quickly approaching its limit and on pace to breach the ceiling in mid-May. The Treasury has a few tools to delay the day of reckoning until early July, when crossing the debt ceiling could lead to the nation defaulting on its debt.

It wasn’t clear from Obama’s comments whether he thought Congress would vote in a single package to raise the debt limit and make spending cuts, or whether Congress would hold a specific vote to raise the debt limit while at the same time exploring ways to make cuts.

Asked in the interview whether he would give in to Republicans’ demand that spending cuts accompany an increase in the debt limit, Obama did not rule out the idea.

“There’s going to be a discussion when the Congress gets back from recess” in late May, he said. “I don’t expect the Republicans to give in and I get 100 percent of my way; and I don’t expect that we’re going to give 100 percent of what the Republicans want.”

Later in the day, White House press secretary Jay Carney said the president thinks the debt limit vote should not be connected to any other vote.

“Congress has to vote to raise the ceiling on our debt. That’s an imperative that shouldn’t be linked or held hostage to any other action because the consequences . . . would be catastrophic,” Carney said.

Obama gave a major fiscal policy speech Wednesday in which he described his vision for reducing the federal deficit by $4 trillion in 12 years.

On Friday, Obama signed into law a 2011 budget approved by Congress this week that slashes $38.5 billion in federal spending while funding the government through the end of September.