Obama said that getting Gadhafi to go away will take a "little bit of time."
"The process of actually getting Gadhafi to step down is not going to happen overnight," he said. "And keep in mind, we've only been operating here for nine days."
Obama strongly defended the U.S. military action in Libya in an address to the nation Monday night as a necessary humanitarian intervention, acknowledging that while America's security was not threatened, U.S. "interests and values" were at stake.
"Some nations may be able to turn a blind eye to atrocities in other countries. The United States of America is different," he said in his speech at the National Defense University in Washington. "And as president, I refused to wait for the images of slaughter and mass graves before taking action."
During his interview with Sawyer, Obama said his administration has been confronted with a series of crises. "We've had more than our share," he said.
"I'm assuming that in future years, things level out a little bit. But in the meantime, this is why I have to do something about the bags under my eyes."
He said that he does "a lot of praying, absolutely, every night, right before I go to bed."
"I am praying that I'm making the best possible decisions, and that I've got the strength to serve the American people well," he said.
The president got in a subtle jab at his critics who took issue with him filling out an NCAA bracket with so much on his plate.
"You know a lot of folks focused on the fact that I filled out my bracket," he said. "Obviously I hadn't been spending that much time studying it since I don't have anybody in the Final Four."
With a nod to Sawyer's Bluegrass State roots, Obama offered congratulations to the Kentucky Wildcats on making it to the Final Four.