"Whether she intends to run for something else, or where she's headed, I'm not privy to that," he said, noting that he is focused on 2010 as opposed to 2012.
"My wife and I like her," Barbour said of Palin, the former Alaska governor. "She's a heck of a lot smarter than she gets credit for."
Barbour, the chairman of the Republican Governors Association, also said Democrats are "whistling past the graveyard" if they don't recognize the lessons from Republican victories in this year's two governors races.
"The American people want us focused on jobs, not on health care reform, not on energy policy," he said, later adding: "You've got 10.2 percent unemployment and no end in sight to the loss of jobs, that's what Americans want the president focused on."
Watch the entire episode, which also includes an interview with Democratic Governors Association chairman Nathan Daschle, above.
More Coverage of Sarah Palin:
Hundreds Line Up for Palin Book Signing
McCain Aide Nicolle Wallace: Sarah Palin's Claims are "Fiction"
Fact Checking Sarah Palin's "Going Rogue"
Marc Ambinder: Palin Needs to Take Herself Seriously
CBS News Poll: Fewer Than 1 in 4 Have Favorable View of Palin
Is Palin Selling Books or Settling Scores?
Exclusive: Palin Accounts Disputed by McCain Aides
Fact Check: Palin Seems to Misrepresent Timeline on Daughter's Pregnancy
Fact Check: Palin Contradicts Her Own Version Of Events With Oprah
Sarah Palin Calls Newsweek Sexist
"Washington Unplugged" appears live on CBSNews.com each weekday at 12:30 p.m. ET. Click here to check out previous episodes.