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This is a RUSH transcript from "The O'Reilly Factor," May 31, 2011. This copy may not be in its final form and may be updated.

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BILL O'REILLY, HOST: In the "Impact" segment tonight: Fox News political analyst Charles Krauthammer, a very outspoken guy, as Donald Trump recently found out. So how does he see this weekend's Sarah Palin bus tour? Charles joins us now from Washington. So Hume and me, your humble correspondent, we feel that she's not going to run. First of all, do you concur?

CHARLES KRAUTHAMMER, FOX NEWS ANALYST: I agree completely. I think it would make no sense for her to run. I think her chances of winning the nomination are small. The chances of winning the general election are probably nil. I think, for the same reasons you articulated, 60 percent negatives. That's almost impossible to overcome. And it isn't as if that is forever. Hillary Clinton had very high negatives at many points in her career. But over time, they tend to soften.

O'REILLY: Yes, but the difference is -- the difference is that the press didn't hate Hillary Clinton, who was promoting her, and the press generally hates Sarah Palin. She's going to have a tough mountain whenever she goes.

KRAUTHAMMER: I'm not sure that Hillary has the political smarts and energy and star power of a Sarah Palin.

O'REILLY: No.

KRAUTHAMMER: So I would not underestimate her. She has a future. Why would you jeopardize it by running now and losing?

O'REILLY: OK. Why do people like George Will, so-called Washington establishment Republicans, not like Sarah Palin?

KRAUTHAMMER: Well, look, I can't speak on behalf of George, but I can speak on behalf of myself as a hoity-toity cocktail-swilling Washington establishment elitist.

O'REILLY: That's what we love about you, Charles, especially the hoity-toity part.

KRAUTHAMMER: Which is actually a phrase she used in her tweet about me. So that's -- I take it as a badge of honor. So I'm not -- so I'll speak on behalf of myself…

O'REILLY: All right. Go.

KRAUTHAMMER: …and the class of hoitys that I represent here. It's not that -- you said in the introduction the rap on her is that she isn't smart. That is not so. She is very smart. And adept. Great political instincts. And is a star. The problem with her, I think, is that she is not schooled. I don't mean she didn't go to the right schools. I mean when you get into policy, beyond instincts -- I like her political instincts. I like her political overall view of the world. But when it comes to policies, she's had two and a half years to school herself, and she hasn't. And that's a problem. You want a president who will be able to not have to learn on the job. We've already had that...

O'REILLY: OK. Let me articulate...

KRAUTHAMMER: ...with President Obama and with others. It's not only -- hold on, one thing. It's not only lack of schooling. It's the lack of effort to school herself and the lack of insight to see that she needs it.

O'REILLY: OK. But I don't really agree with you on that, and let me tell you why. I think the woman is shrewd. Shrewd. I think that's the word. And she's savvy in the political world. And she obviously ran the state of Alaska pretty well. Her approval rating was high and she did a lot of stuff with the folks with the oil companies getting them money. But her frame of reference is weak. And that's what I say the rap on her isn't she isn't smart; is that when she gets into the Korean War or when she gets into how the Cold War influences policy today or how the Muslim world evolved into an enemy of the United States, all of these things she has trouble with, and that's -- that's what the rap on her is. She simply doesn't know enough about the world to be able to govern at that level. Do you agree or disagree?

KRAUTHAMMER: No, I agree with you about that. I think if you're going to master policy, especially world affairs, you've got to know history. As you said, you have to know how things evolved, and she is weak on that. It's not as if she can't learn. The fact is it doesn't appear as if she wants to sort of sit down, spend some months schooling herself, as many people have done in preparing for the presidency. If you're a governor of any state, you face a narrow range of issues, and you don't have to deal with the world. It's incumbent on you to actually learn about it.

O'REILLY: OK, the final thing is that, up against Michele Bachmann -– we're having this interesting BillOReilly.com poll. It's the same constituency: conservative Tea Party people with a little bit of general conservative people. Who do you think is going to come out on top on that?

KRAUTHAMMER: Well, there was one on "Special Report" the other night, and Bachmann came slightly ahead of Palin. I think it was like 55 to 45. I think you'll probably get a slight Bachmann advantage, simply because she's new and fresh. She is in Congress, so she's actually on the scene, has more of a sort of a grounding, has been out there casting the votes and is more current. I don't know that it portends for the future, but I think if you had them both in the race, they would actually harm each other and allow others to pass them in the field.

O'REILLY: OK, Charles. Thanks, as always. We appreciate it.

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