"To besmirch her reputation is outrageous," Mr. Obama said.
Rice is under fire from some Republicans for initially stating in television interviews that the September attack on an American Consulate in Libya appeared to be the result of a spontaneous demonstration.
"As I've said before she made an appearance at the request of the White House in which she gave her best understanding of the intelligence that had been provided to her. If Senator McCain and Senator Graham and others want to go after somebody they should go after me," Mr. Obama said.
And that's just what Senator John McCain, R-Ariz., did a short time later. He has been one of Rice's fiercest critics.
"First and foremost, the president of the United States, the commander in chief, is the most responsible, and I hope the president has no illusions about our view of his responsibility, which I believe are those of the American people as well," McCain said.
Mr. Obama was also asked about the most pressing economic issue facing him and the Congress - the negotiations over the fiscal cliff.
Mr. Obama was also asked about the most pressing economic issue facing him and the Congress: the negotiations over the fiscal cliff.
"What I'm not going to do is to extend Bush tax cuts for the wealthiest 2 percent that we can't afford, and according to economists, will have the least positive impact on our economy," Mr. Obama said. "A modest tax increase on the wealthy is not going to break their backs; they'll still be wealthy."
The president says he will improve his relationship with Congress and members of the Republican Party.
"I think all of us have responsibilities to see if there are things that we can improve on and I don't exempt myself from needing to, you know, do some self-reflection and see if I can improve our working relationship."
The president also said he would pursue immigration reform and climate policy.
CBS News Political Director John Dickerson said it struck him when the president said he was mindful of second-term presidents who overreach.
"So there was a part of him when he was restrained yesterday, but the part that wasn't when he took a whack at Senators McCain and Graham. That stood in contrast from the reserved approach he took to taxes even saying he was being self reflective about dealing with Congress."
Dickerson also discussed a new round of remarks made by Mitt Romney to donors where he dissected his beliefs as to why Mr. Obama won.
"[Romney said] the president did well with minorities - African Americans, Hispanic voters, young voters - because he systematically bought them off. With young voters he talked a lot about college loans. With Hispanic voters, having younger Hispanic voters... give them citizenship. With African American voters one aide suggestions said it was the lowering of welfare requirements. This was the sentiment at the heart of that secretly recorded video where he talked about the 47 percent. Romney spent several weeks trying o walk back from that statement now he seems to be embracing it again."
Dickerson added: "The reason you would embrace this argument if you were in the Romney camp is that the alternative argument that they totally misread the electorate is a much more painful argument to embrace."