This is a partial transcript of "The Big Story With John Gibson," Nov. 5, 2004, that has been edited for clarity.

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(BEGIN VIDEO CLIP)

UNIDENTIFIED REPORTER: Tell us about your political future, Senator?

HILLARY RODHAM CLINTON (search) (D), SENATOR, NEW YORK: I'm having the best time being the Senator from New York.

(END VIDEO CLIP)

JOHN GIBSON, HOST: Right. President Bush's re-election victory is only a few days old, but we're already looking ahead to the next for the White House.

Heather Nauert is here with a look at the some of the possible candidates. Hi, Heather.

HEATHER NAUERT, FNC CORRESPONDENT: Hi there, John.

Well, of course, just when we thought we were done talking about politics, of course it's never too soon to start talking about the next election and who is going to try to position himself or herself for the White House.

I'm joined by Mark Preston (search), a Senior Staff Writer for "Roll Call" newspaper. And that's the big question today, Mark: who is eying the White House for 2008?

MARK PRESTON, SENIOR STAFF WRITER, "ROLL CALL": Well, there's a long list on both sides of the aisle. You showed the clip from Hillary Clinton. She's certainly topping the list. There's a lot of liberal Democrats out there that would love to see Hillary Clinton run.

On the Democratic side as well, you see somebody a little bit more to the middle. Evan Bayh, who is considered a centrist and somebody that, certainly, Democrats, who are dismayed at what they saw in this past election, would like to see run; someone who can maybe appeal to middle America, perhaps the South. Two areas where Democrats did very poorly, of course, on Tuesday.

NAUERT: And Evan Bayh (search) is a popular guy, a Midwestern Senator and also served as governor. But let's talk about that sexier candidate for a second, Hillary Clinton.

How on earth can the Democrats not nominate her? She has spent a lot of time this year stumping for the candidates, raising money, campaigning for them. How can they not?

PRESTON: Well, I tell you what, Hillary Clinton certainly did a lot. She was a good foot soldier for Democrats over the past couple of years, raising money, as you say, and out there on the stump.

But there is some concern in the Democratic Party right now that they lost the election on the values issue. It's really not real clear why the Democrats lost several seats in the Senate, a few in the House, and as well as failing to unseat Mr. Bush.

It could have been the war in Iraq. It could have been a confluence of a lot things, but a lot of people think that the Democratic Party might be too liberal and, if that's the case, then Hillary Clinton wouldn't be the candidate for the Democratic Party to put out there.

NAUERT: And that makes Evan Bayh, as you mentioned, a more palatable candidate. What kinds of things will Edwards do to try to keep his name out there? Because there's been a lot that's been talked about him in the past few days, that he's really trying to set the stage for 2008.

PRESTON: You know, interestingly enough, I don't know what John Edwards (search) can do. Certainly in the short term I'd expect that we'd see him not do very much. His wife was diagnosed with cancer the other day, so I think he's probably going to tend to that.

I would expect you would see John Edwards out there on the speaking circuit anyway, certainly making his way around. Don't be surprised to see him in Iowa or New Hampshire, sooner rather than later, appearing before dinners or breakfasts trying to talk to activists, trying to make early inroads.

A couple of other big...

NAUERT: Is he a dead duck? Are we going to see him again?

PRESTON: No, he's not a dead duck and I think it's too early to say anyone is a dead duck at this point. But, I think Democrats might even look out to the states.

Don't be surprised, too, to see Democrats look at Iowa Governor Tom Vilsack (search) or perhaps New Mexico Governor Bill Richardson (search), maybe get outside of Washington to look for their candidate.

NAUERT: OK. And let's talk about the Republican side.

We hear a lot of talk about Rudy Giuliani (search) and John McCain (search), but are they necessarily conservative enough to appeal to the conservative base that, as we have seen through this election, is so important to Republicans?

PRESTON: Well, I'll tell you what. They are two great names to talk about and you will certainly hear them over the next three years. The problem with Giuliani is, of course, his social views and that is not going to sit well with a lot of the Republican-based voters.

The problem with McCain is a lot of the real conservatives don't like John McCain even though he is conservative. He is not somebody that is in lock step with the Republican Party and he has shown that over the last couple of years.

A couple of other names out there that I think you're certainly going to see is someone such as Senate Majority Leader Bill Frist (search). He will retire in 2006. He'll have two years now to run for the presidency, and we think he is going to do that, as well as Senator San Brownback...

NAUERT: He has really had a lot of political capital right now. He, just like Hillary Clinton, was out spending a lot of money, which you really can't understate how important that is to getting the faithful people from the party to back them. Is that right?

PRESTON: Absolutely. He was out there, he was raising money, he was stumping for candidates. He even went into South Dakota to stump against Senate Minority Leader Tom Daschle (search), which proved successful but very controversial.

Another person you will see because of that, trying to ride a little bit of the sweep from 2004, is George Allen (search). He's a former Virginia governor who is running for a second term. He will likely win in 2006. So he is someone who's going to look, as well.

NAUERT: OK. And what about Jeb Bush (search) and some of the others from the state level?

PRESTON: Sure. You want to talk about a dynasty. I guess Jeb Bush has said he does not want to run, but things can change. Certainly his brother did very well this past week. He's someone who is very popular down in Florida. Jeb Bush could certainly be a candidate even though he says now he might not be.

I think if you even had just looked here in Washington, what would be really interesting is to see who is really going to run for that conservative vote, the real religious, perhaps moral, vote. I think that you're going to see Frist, Senator Rick Santorum (search) and Senator Sam Brownback (search), all trying to vie for that.

NAUERT: All right. Mark Preston of "Roll Call", we're going to have to leave it there. We have at least six other names that we didn't get a chance to get to, so maybe next time. Appreciate it.

PRESTON: Four more years.

NAUERT: All right. Plenty of time. John?

GIBSON: All right, Heather. Thanks very much.

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