Hillary Clinton puts a foot out the door

Two decades as one of the most recognizable faces of the Democratic Party may have finally caught up to Secretary of State Hillary Rodham Clinton.

"It would be a -- probably a good idea to just find out how tired I am," she told a gathering of State Department employees Thursday. The remark drew laughter.

She also claims political fatigue has kept her from watching any of the Republican presidential debates.

Still, she says she's committed to her current position.

"I have made it clear," she said, "that I will certainly stay on until the president nominates someone and that transition can occur."

But speculation that Clinton and Vice President Joe Biden might swap jobs continues to swirl, albeit with minimal sourcing.

Clinton: I want to step off political "high-wire"

That's not impossible, observes Bill Clinton's former labor secretary, Robert Reich, pointing out, "It would be good for the president, good for the party, more importantly, good for the country."

Clinton and Biden both have rejected the idea. She said previously she has "absolutely no interest and no reason to do anything other than dismissing these stories and moving on."

"Biden has said, "Hillary likes her job where she is. I like my job where I am"

And Clinton's close friends call it highly unlikely. One, Lanny Davis, says, "I've known her for 40 years. When she says something, she means it. She's had a great time as secretary. I know she wants to be with (daughter) Chelsea and President Clinton and relax awhile. I want her to be happy."

But, always the clever politician -- following her remarks about being tired -- the secretary gave us just enough to keep on guessing, saying, "Everyone always says that (that they want to rest) when they leave these jobs."

A recent Bloomberg poll shows nearly two-thirds of Americans have a favorable view of Mrs. Clinton.

Still, she has said in numerous interviews that she will not serve a second term as secretary of state, and won't run for president in 2016.

To see Whit Johnson's report, click on the video in the player above.

CBS News chief Washington correspondent and "Face the Nation" host Bob Schieffer says the president would only ask Hillary Clinton to be his running mate instead of Joe Biden if Mr. Obama felt he absolutely had to to win: