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This is a RUSH transcript from "The O'Reilly Factor," July 19, 2011. This copy may not be in its final form and may be updated.

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BILL O'REILLY, HOST: In the "Back of the Book" segment tonight: New York Post columnist Cindy Adams writes today that Sarah Palin may very well run for president. Ms. Adams citing the governor's intense study routine as evidence she is preparing for the fray. Joining us now from Washington to analyze that possibility, and also the Rick Perry factor, Fox News analyst Charles Krauthammer. So if Governor Palin does get into the race, what happens?

CHARLES KRAUTHAMMER, FOX NEWS CONTRIBUTOR: Well, it gets very interesting, it gets very complicated, and the rowboat gets very crowded. Bodies are going to start to go overboard. If you look at the latest polls, you've got only four candidates, potential candidates, in double digits. You've got Romney at 25, Bachman at 14, Palin at 12, Perry at 10. Now, if you look -- that means that if Palin enters the race, she and Bachmann are going to fight it out for mostly the same constituency, and that is not -- it's not a question of sexism or gender. It's a question of who their constituencies are. They are both strong with the Tea Party. Bachmann is the head of the caucus in the House. Palin, of course, supported it, is very strong among Tea Partiers, exploited that, used that to her advantage in helping a lot of candidates in the midterm elections. So if you add up their percentages, they're roughly equal to Romney. One of them would emerge as the major opponent. And right now...

O'REILLY: Well, I think you're right. I don't think Sarah Palin is going to take any votes away from Mitt Romney. It's a whole different...

KRAUTHAMMER: Exactly. It's a whole different constituency.

O'REILLY: Right now Michele Bachmann, and we have a report on her tomorrow because there was some little thing in South Carolina that we're trying to sort out right now before we report it. We don't want to put on erroneous information involving an ABC News correspondent. Michele Bachmann has some momentum, particularly in Iowa, where she's a favorite daughter, born there. And I -- look, Cindy Adams is often right about what she puts on paper. And so you have to take this seriously that she mentioned that she believes, Cindy Adams, that she's going to jump in. But I agree with you that if Sarah Palin does jump in, Palin and Bachmann pretty much neutralize each other and Romney benefits.

KRAUTHAMMER: Well, exactly. It's as in the poll. They split that constituency. You'd imagine that if Palin were to stay out that would increase the Bachmann vote.

O'REILLY: No doubt about it.

KRAUTHAMMER: Because people would go to her.

O'REILLY: Who's stronger: Palin or Bachmann?

KRAUTHAMMER: Well, it's interesting. If you'd asked anybody six months ago, you know what the answer would have been. Bachmann is a phenomenon. It's sort of like the phenomenon that we had in 2008 with Huckabee, who was unknown. He was way down in the polls. He performs well in a couple of debates. All of a sudden he's a first-tier candidate. That is the story in almost every cycle. Somebody comes out of the pack. She has -- now she came out really early. It was only in one debate. So we're going to have to see if she might have peaked early. Now expectations are really high for Bachmann. Nobody would have said three months ago she has to win Iowa. I think now the expectation is she wins Iowa.

O'REILLY: Right. Frontrunner, sure.

KRAUTHAMMER: If she doesn't, it's going to look like a defeat.

O'REILLY: And it will be. She should win Iowa, that caucus.

Now, Rick Perry, Texas, indicating that he will jump in the race at the end of the summer. He is a threat to Mitt Romney, correct?

KRAUTHAMMER: I think he is. I think there's going to be somebody coming out of the existing pack that will be one contender against Romney. Perry, I think, on his own could be the other contender against Romney. It would be three-way race. He comes in as a man, obviously, with a lot of experience as a governor, executive experience. He's strong with the social conservatives. And Texas has had a good record. Thirty-seven percent of all the new jobs in the recovery have been in Texas. And he's got a lot of money. You put that all together, you have got a serious contender against Romney. I think it becomes a three-way race.

O'REILLY: And the hair. Both of their hair looks the same. So somebody might get mixed up.

KRAUTHAMMER: Presidential -- presidential hair.

O'REILLY: Got the hair going on there.

KRAUTHAMMER: Presidential hair of the Reagan.

O'REILLY: The Reagan hair. All right. So are you going to predict that Perry will jump in?

KRAUTHAMMER: Absolutely. I'll go with that one.

O'REILLY: OK. So you say Perry is in, becomes a three-person race then. Perry, Romney and whoever emerges from the Palin-Bachmann, but most likely congresswoman because Sarah Palin, good chance she doesn't get in because of the very reason that her constituency is split now.

KRAUTHAMMER: Right.

O'REILLY: All right. Charles, always interesting. Thank you very much.

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