Despite that, Schieffer said, Mr. Obama gave "about as good a speech as I've heard him make," offering a rationale for why the Nobel Peace laureate had just ordered an increase of U.S. forces in Afghanistan.
"He was accepting a prize that many people thought was not given to him for what he had done, but was basically a slap in the face at the Bush administration," Schieffer told "Early Show" anchor Maggie Rodriguez.
"And he admitted during this speech — I think he had to — he said, look, there are a lot more people, many, many people around the world who deserve this far more than I do. He also had to lay out a rationale for a war that many in Europe think is not worth fighting.
"But I thought the key paragraph was, 'I face the world as it is and cannot stand idle in the face of threats to the American people.'"
Despite positive comments on the speech from even his right-wing critics, including Newt Gingrich and Sarah Palin, the president still faces sagging poll numbers — according to a new CBS News poll his approval rating is the lowest it's ever been, now standing at 50%, down from 53% last month.
Rodriguez asked what the president needs to do to stop this decline.
"Well, this presidency and what history writes of it will not depend on how many prizes he wins," Schieffer replied. "It will depend on what he does about the economy and bringing this war in Afghanistan to some kind of conclusion.
"People keep saying the president has so many things on his plate, but the thing about the presidency is the president doesn't get to decide what's on his plate. Events decide that. And this president is facing a lot of very severe problems.
"When unemployment starts to go down, his approval ratings will start to go up — and it's just about that complicated," Schieffer said.
More on Obama's Nobel Prize:
Obama: U.S. Standard Bearer for Peace
Obama Offers Treatise on War and Peace
Obama Channels George W. Bush
Photos: Obama in Norway
Full Text of Obama's Remarks
Video: Obama's Nobel Prize Speech (excerpts)
Analysis: Can Obama Deliver on Nobel Peace Prize Goals?
Who Should Get Obama's Nobel Prize Cash?