"I think we've got to think it through," he said. "But I have to reiterate once again that we only have one president at a time. And I want to be very careful that we are sending the right signals to the world as a whole, that I am not the president and I won't be until Jan. 20."
Obama also joked about taking advice from former presidents.
"In terms of speaking to former presidents, I have spoken to all of them that are living," he said. "Obviously, President Clinton. I didn't want to get into a Nancy Reagan thing about, you know, doing any seances."
The remark prompted chuckles at the press conference. But later, Obama reached out to express regret to the widowed former first lady, who's recuperating from breaking her pelvis, Obama transition team spokeswoman Stephanie Cutter said in a written statement.
"President-elect Barack Obama called Nancy Reagan today to apologize for the careless and off-handed remark he made during today's press conference," the statement said. "The president-elect expressed his admiration and affection for Mrs. Reagan that so many Americans share and they had a warm conversation."
Incidentally, Nancy Reagan never held a séance at the White House, though she was reported to have consulted with an astrologer when planning her husband's schedules.
While he may not have revealed any more details about his Cabinet, Obama did reveal some important information about the topic that has generated the most interest on his Web site -- his daughters' dog.
"With respect to the dog, this is a major issue," he said. "I think it's generated more interest on our Web site than just about anything. We have two criteria that have to be reconciled. One is that Malia is allergic, so it has to be hypo-allergenic. There are a number of breeds that are hypo-allergenic. On the other hand, our preference would be to get a shelter dog.
"But obviously, a lot of shelter dogs are mutts, like me," he said. "So whether we're going to be able to balance those two things, I think, is a pressing issue on the Obama household."