This is a rush transcript from "The Big Story With John Gibson and Heather Nauert," January 28, 2008. This copy may not be in its final form and may be updated.

JOHN GIBSON, CO-HOST: Mitt Romney has caught up to rival John McCain in the Florida polls. Right now it looks like tomorrow's primary is going to be a two-man race. Romney is touting himself as the conservative candidate, slamming McCain's campaign finance reform bill, his stand on immigration and his support of an energy bill as being too far left for Republicans.

So what's it going to take for Romney to win over voters in the Sunshine State in this final push?

The governor's senior foreign policy adviser, Liz Cheney, the vice president's daughter, is here now in her first live interview on FOX since signing on to Romney's campaign.

So Liz, you were a Thompson supporter. Obviously, he's out of the race. Why did you pick Romney?

LIZ CHENEY, ROMNEY SENIOR FOREIGN POLICY ADVISER: Well, it's great to be here. Thanks, John. I think that clearly, Gov. Romney, when you look across the whole range of issues and challenges our next president is going to have to face, is the one best suited to face those challenges. He has got a very clear record on issues like cutting taxes. Sen. McCain also voted against the Bush tax cuts in 2001 and 2003, for example, in addition to the list you mentioned before.

But Gov. Romney understands what it takes. He was out in the private sector very successfully running a business for 25 years. He turned the Olympics around. He was a very successful governor in Massachusetts. So, on economic policy, on social issues and on national security policy where he understands absolutely we have to win in Iraq. He understands the larger global war on terror and what it will take for us to prevail there. As I looked at the candidates, it became clear to me, absolutely that Gov. Romney was the man who would best lead this country.

HEATHER NAUERT, CO-HOST: Liz, can you answer this? Some of his critics have said that he changes positions really just to fit his audience. So what do you say to those folks who are concerned about that, or feel that way?

CHENEY: Well, I would say you need to take a look at his record and not just sort of listen to the rhetoric. We're hearing a lot of attacks flying, especially now, given how close and intense this race in Florida is. But I think if you look at issue after issue after issue, at the governor's record, at what he has accomplished, as governor of Massachusetts in the private sector, the allegation of flip-flopping is one that, you know, is a popular one politics that I don't believe it fits well here or does any service at all to the governor's real record. And let me just say that ...

NAUERT: Well, John McCain just came out with a pretty tough ad - this new web ad called "A Tale Of Two Mitts," that's what they're calling it, saying he's changed his position on abortion, and a whole host of issues. So, what do you say to all that?

CHENEY: Well, I would say, first of all on the issue of abortion, Gov. Romney has been very straightforward about that. He is pro-life; he's been pro-life since he was governor of Massachusetts. You know, I think you've got to stack that up against Sen. McCain's record where he's taken positions that have been wrong and he's kept those positions.

If you look just at the issue of the tax cuts, for example, where he voted against the Bush tax cuts twice, when he was asked recently about the vote, he said he would vote the same way again, so Sen. McCain's positions, I think, give a lot of conservatives real concern and cause for concern.

GIBSON: Liz, you know, in the head-to-head polling, McCain is the one that always shows up beating either Hillary or Obama, and others do not, including Romney. We know you have endorsed Romney, but can Mitt beat Obama or Hillary in the poll?

CHENEY: I think there's no question. You know, those head-to-head polls that are taken during primary season really don't mean very much. I think once we've got a nominee, that's when the real head-to-head match-up matters. And I think frankly, Gov. Romney as our nominee is much more likely to turn out the conservative base and turn out voters that Republican needs to win and has needed to win over the past several elections. I think that there's a real question about whether Sen. McCain would be able to turn those voters out. So I have no question at all in my mind about Gov. Romney's ability to prevail in November.

GIBSON: I have to ask you about national security. I mean the Cheney name is closely associated with the issue of national security. Does Mitt Romney really stand the Cheney test of national security?

CHENEY: I think that, again, I wouldn't be endorsing him if he didn't. I assume you mean the Liz Cheney test, John.

GIBSON: Absolutely.

CHENEY: I think that Gov. Romney, clearly, when you look at his position on Iraq, when you look at his position on the issue of the larger war on terror, and I would say when you look at issues like the importance of the United States being able to hold terrorists at Guantanamo in Cuba, which is something that Sen. McCain has questioned and has suggested we ought to bring those terrorists back to the United States where, in fact, on U.S. territory, they would get access to our court systems, access to lawyers.

Gov. Romney understands that that's actually a dangerous approach. And so I think if you look at the whole range of issues that have to do with our national security, I feel very confident and very good about where Gov. Romney is on those issues.

NAUERT: All right. Liz Cheney, Mitt Romney's senior foreign policy adviser and a big supporter of his. We thank you very much.

CHENEY: Thank you. Very good to be with you guys.

Content and Programming Copyright 2008 FOX News Network, LLC. ALL RIGHTS RESERVED. Transcription Copyright 2008 Voxant, Inc. (www.voxant.com), which takes sole responsibility for the accuracy of the transcription. ALL RIGHTS RESERVED. No license is granted to the user of this material except for the user's personal or internal use and, in such case, only one copy may be printed, nor shall user use any material for commercial purposes or in any fashion that may infringe upon FOX News Network, LLC'S and Voxant, Inc.'s copyrights or other proprietary rights or interests in the material. This is not a legal transcript for purposes of litigation.