Obama said if he wants to nominate Rice, he will.
Obama spoke about Syria after France became the first Western nation to recognize the new opposition group as the only legitimate representative of the Syrian people.
"We're not yet prepared to recognize them as some sort of government in exile," Obama said. "But we do think that it is a broad-based representative group."
The Libya episode is also entangled with the sudden career fall of the CIA chief at the time, David Petraeus. He resigned last week after disclosing an extramarital affair that had been uncovered during an FBI investigation into another matter. The same scandal has also put a cloud on the Afghan war commander, Gen. John Allen.
Obama said he hoped the scandal would end up being but a "single side-note" in Petraeus' stellar career. He was more measured in his defense of the FBI and in the way he was just notified about the Petraeus investigation last week, saying he was withholding judgment until more facts come.
Between the personnel controversy and the effort to prevent a fiscal crisis on Jan. 1, Obama conceded he had not had much reflection on the campaign.
"I think everybody forgets that the election was only a week ago," he said. "I know I've forgotten."
He said he still plans to reach out to his Republican rival, Mitt Romney, to get ideas on improving the government and the economy. And, yes, he must work better with Congress.
"All of us have responsibilities to see if there are things we can improve on," he said. "I don't exempt myself from needing to, you know, do some self-reflection."
Obama won a second term handily in the Electoral College, but about 48 percent of the voting public wanted Republican Mitt Romney in office instead.
"I'm more than familiar with all the literature about presidential overreach in second terms," Obama said.
He said the only mandate he got from voters was simple — "work really hard to help us."