He has yet to make a decision as to who to nominate for secretary of defense, Obama said.
Sources have said they think the president will pick Chuck Hagel, a Republican, who has met with controversy since his name has been connected with the position.
Gay rights groups, which were strong supporters of Obama's election campaigns, have hit Hagel for questioning in 1998 whether a nominee for an ambassadorship was suitable because he was "openly, aggressively gay."
Obama, without calling Hagel his preferred candidate for the job, said: "I've served with Chuck Hagel (in the U.S. Senate). I know him. He is a patriot. He is somebody who has done extraordinary work."
Hagel has apologized for those comments, Obama said. He added that he didn't see anything in Hagel's political record that disqualified him as a potential nominee.
Hagel currently is the co-chairman of the president's Intelligence Advisory Board. Leon Panetta, who has been secretary of defense since July 2011, has indicated he wants to return to private life next year.
Four issues for the next term
When asked about his priorities for the next four years, Obama listed immigration, the economy, energy and debt reduction.
He will introduce legislation to fix a broken immigration system in 2013, he said.
"We have talked about it long enough," He said. "We know how we can fix it."
Obama also wants to fix America's infrastructure.
"If we are putting people back to work, rebuilding our roads, our bridges, our schools, in part paid for by some of these broader long-term deficit reduction measures that need to take place, that will grow our economy," he said
And he wants to increase further the amount of energy, especially green energy, that America produces.
"We are producing more energy and America can become an energy exporter. (The question is) how do we do that in a way that also deals with the environmental challenges that we also have at the same time," Obama said.
But the most pressing quandary is the fiscal cliff.
"It is going to be very hard for the economy to sustain its current growth trends if suddenly we have a huge bite taken of the average American's paycheck," he said.