This is a partial transcript of "The Big Story With John Gibson," June 30, 2005, that has been edited for clarity.

JOHN GIBSON, HOST: His dad was president. His brother is president. Now there are all kinds of speculation that Florida Governor Jeb Bush (search) could make a run for the White House. But is a name enough to beat an 800-pound gorilla named McCain?

Joining me now is Republican strategist Brad Blakeman and Democratic strategist Chris Lehane.

Welcome to you both.

BRAD BLAKEMAN, REPUBLICAN STRATEGIST: Thank you, John.

GIBSON: Chris, let me go to you first.

Now, you know, Jeb Bush has sworn this off, I mean, at least publicly. Now, people swear these things off all the time and then do it anyway. But he said he doesn't want to be part of any dynasty. In what circumstances could you see a guy who has sworn it off, who is afraid of the "D" word, doesn't want guys like Chris Lehane accusing him of constructing a dynasty — what circumstances could he set all that aside and say he'll go for it?

CHRIS LEHANE, DEMOCRATIC STRATEGIST: Well, I think power always has a certain elusion to it. And, you know, this is a guy who is governor right now. His brother is president. You could certainly see him becoming enamored with being president of the United States. It's a very powerful position, obviously.

You know, I think it will be an extremely tough thing to pull off. The president obviously is not particularly popular these days. And if you run with Bush as your last name, you are going to have an awful lot of explaining to do. I think that he would have the potential to be an extremely strong primary candidate, but an exceedingly weak general election candidate.

GIBSON: Brad, first of all, that analysis by Chris, you buy it?

BLAKEMAN: No. Governor Bush is more than a name. Let me remind Chris that, in 1992, we had a governor of Florida who was a Democrat. Both houses were controlled by the Democrats. Today, both houses are controlled by the Republicans. And Jeb Bush was the first Republican re-elected as governor, great record. So, there is a lot more than the name. And I think Jeb Bush will be a formidable candidate, if in fact he decided to run.

GIBSON: Well, Brad, what about the McCain factor? I mean, you know, you only have to pick up the press and see McCain is running and he is the big dog. And he has got a few very conservative Republicans that don't seem to like him, but, arguably, he is one of the most popular politicians in the country. Can Jeb Bush overcome McCain?

BLAKEMAN: I think Jeb Bush would be a formidable candidate.

On the other hand, Senator McCain (search) is a formidable candidate. But we have to remind ourselves, in our system, you have to be selected before you are elected. And lot has to happen in the primaries before you are sworn in to that office.

GIBSON: Chris, are the Democrats worried about McCain more than Bush?

LEHANE: I think what you are going to see happening on the Republican side is a continuation of what you've seen happening in the last six or seven months, which is that the right wing of the party, the conservatives, the special interests, are going to continue to push this party farther and farther and farther away from the mainstream.

And, as a result of that, I think the Republican primary is going to be an absolute bloodbath for each of these various candidates.

(CROSSTALK)

GIBSON: Chris, I'm having a little difficult time what mainstream you are talking about. The Republicans seemed to have the mainstream nailed down pretty good last time.

LEHANE: Well, you look at a president whose approval ratings are in the high 30s, which is a very, very, very poor rating.

BLAKEMAN: What polls are you looking at, Chris?

(CROSSTALK)

LEHANE: You look at a president whose entire political agenda is stalled right now in Congress because it is out of the mainstream.

You look at a party that is not talking about the issues that impact the middle class: high gas prices, dealing with the jobs that are going overseas, dealing with the fact that Usama bin Laden (search) is still running around out there making more videotapes than MTV does.

GIBSON: Brad, make your points now, before I run out of time.

(CROSSTALK)

LEHANE: ... and you worry about.

GIBSON: Brad, make your points now, before I run out of time.

BLAKEMAN: Well, this guy is completely out of touch. How about the energy bill that just passed the Senate? There are a lot of things President Bush has done and is going to continue to do.

LEHANE: Where's Social Security?

(CROSSTALK)

BLAKEMAN: Don't underestimate...

LEHANE: What's the president doing on gas prices?

(CROSSTALK)

BLAKEMAN: Don't underestimate the president.

LEHANE: Why are two out of three countries on the axis of evil arming themselves with nuclear weapons under this president's watch?

GIBSON: On this note, I'm going to let those two guys continue to argue.

Chris Lehane, Brad Blakeman, thanks to both of you. Appreciate it.

(CROSSTALK)

LEHANE: Take care.

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