This is a rush transcript of "Special Report With Brit Hume" from May 22, 2008. This copy may not be in its final form and may be updated.

(BEGIN VIDEO CLIP)

JOHN MCCAIN, (R) PRESIDENTIAL CANDIDATE: My principle on that issue is someone who shares my values, my principles, my goals, and my priorities for America.

(END VIDEO CLIP)

BRIT HUME, HOST: What is that man talking about? Why, he's talking about possible candidates for vice president, and he's having a little event this weekend, a little cookout at his place in Sedona, Arizona, a legendarily picturesque spot where McCain is supposed to be terrific at a barbecuing, and some of the people on the short list who we mentioned earlier in the program will be there.

Some thoughts on the choices facing McCain now from Jeff Birnbaum, columnist for The Washington Post, and Mara Liasson, National Political Correspondent of National Public Radio, and the syndicated columnist Charles Krauthammer, FOX News contributors all.

Mara, this stuff is right up your alley. What do you think?

MARA LIASSON, NATIONAL CORRESPONDENT, NATIONAL PUBLIC RADIO: Well, I think this is, first of all, quite early for him to begin this process, and I don't think what is happening this weekend are actual vice presidential interviews.

But there are a lot of names on his list, and there are a lot of names that, while they sound good, I don't think are possible. Bobby Jindal is one of the most interesting on this list. He is 36-years-old. He has no foreign policy experience —

HUME: Other than a couple years in the House and voting on issues.

LIASSON: — a couple years in the House — and lack of experience is going to be John McCain's big brief against Barack Obama. And because John McCain is going to be 72-year-old, if he's elected, he has to have someone who can step in immediately. And I don't think that's 36-year-old foreign policy novice is it.

Charlie Crist, I think —

HUME: He's the governor of Florida.

LIASSON: — the governor of Florida.

HUME: His picture will presently appear on the screen. There it is.

LIASSON: I question if McCain needs him to win Florida. He's running so well there in the polls. He also might not be conservative enough for some of the party.

HUME: Jeff, your thoughts.

JEFF BIRNBAUM, COLUMNIST, THE WASHINGTON POST: Well, Mitt Romney is going to be there, and I think he probably is on the short list — the former governor of Massachusetts.

HUME: You don't think the apparent lack of personal chemistry between the two gentleman is an obstacle?

BIRNBAUM: I think it is an obstacle, and it is more than an apparent lack of chemistry.

But I do think that this social event and a previous appearance — they traveled together a month or so ago — I think it might be helping. Maybe Romney would be a good choice.

But I agree with Mara. I have spoken to the McCain campaign, and they are adamant that this really is a social event, and it probably is a social event, and it is a way for McCain to get to know them.

HUME: It is not an accident.

BIRNBAUM: No, it is not.

HUME: If it was a social event then he would invite a bunch of his buddies. But these are political figures who happen to be getting the word from the great mentioner, including people like us, that they're on the list, right?

BIRNBAUM: They are.

I think that serious interviews will come later, and, in fact, that McCain's own decision will come later, because the Democratic Convention comes first, and McCain will have the luxury of reacting to whoever Barack Obama chooses as his vice president in choosing his running mate.

And I think that will be a factor that he will be more than happy to wait for.

HUME: It is extremely important, however, Jeff, for you to make clear that he will be doing a lot of thinking about this in the weeks ahead, because we need to talk about something. And if you are just saying here that this is moot until September, then we're in trouble here.

BIRNBAUM: No, this is a very important barbecue, very important.

CHARLES KRAUTHAMMER, SYNDICATED COLUMNIST: And we remained seized of this issue and will be for months because of its importance.

McCain has to decide what kind of election he thinks he will have. If it's a long-shot election, then the advice he is getting of thinking outside the box — of Jindal or somebody unknown and exciting, is a good idea.

But I think actually it's a terrible idea, because it's not going to be a long-shot. I think he is a competitive candidate even in a Democratic year.

HUME: So he doesn't need to throw a long ball.

KRAUTHAMMER: He shouldn't throw a long ball because it's risky. Look what happened with Mondale in '84. He knew he had to throw a long ball, and he picked Ferraro, the first woman, and it actually was a drag on the candidate —

HUME: Because the controversy of her family's money, the financing.

KRAUTHAMMER: No, not because of her intrinsically, but she had baggage, and it turned out to be not a good move.

So why would you throw a long ball in a campaign in which you're running even or even ahead, occasionally, of Obama.

HUME: Who sounds like a plausible choice for you?

KRAUTHAMMER: Well, it is a "do no harm" choice. I think either somebody bland and presentable like a Portman, Rob Portman.

HUME: But doesn't his connection to the Bush administration make it hard?

KRAUTHAMMER: Yes, but it's tenuous.

HUME: He is a member of the cabinet!

KRAUTHAMMER: But it's the budget office. It's not exactly a political office. It is a guy who is cutting checks, essentially.

Or a Crist, or, I think, a Romney, a guy who won't bring a state, but he's clean as you can get. The guy doesn't drink coffee. He has been vetted. And he has this economic appeal because, obviously, he is a guy who can manage and who has done stuff in the past.

You go for a safe choice who will not harm you.

HUME: It suggests then that a weekend social barbecue is a particularly important opportunity for Romney to smooth his relations, perhaps, with McCain.

LIASSON: I think the bad chemistry is the least problem.

HUME: Really?

LIASSON: I really do. I think people who don't like each other run on tickets together many, many times. Lyndon Johnson and John Kennedy, and Ronald Reagan and George H.W. Bush for that matter.

HUME: They ended up being pretty good friends.

LIASSON: They ended up fine, but not at the beginning.

And I think the problem with Romney, Fred Barnes has said on this show that the combination of McCain and Romney pulls poorly and doesn't help McCain. And when I inquired about this today, it was the Mormon issue is still a problem for him. And also Romney ended his campaign, although conservatives were warming to him, he ended his campaign with a net negative favorability rating.

BIRNBAUM: I think a governor is a very strong possibility, somebody from outside Washington. One name that we should mention is Tim Pawlenty of Minnesota —

HUME: Well, there are questions about that, but he couldn't have gone anyway because of a wedding, apparently, and he has some other visit down there with McCain. So he has been through the social — before.

He's an appealing young guy, and I guess he would leave Minnesota and help with that win.

BIRNBAUM: Which could be a very important state. In fact, the Midwest will be a very important battleground.

HUME: Interesting stuff, thank you, panel.

When we come back, Iraqi troops score a major success in Shiite militia stronghold of Sadr City. We'll talk about the recent developments there when we come back.

(COMMERCIAL BREAK)

(BEGIN VIDEO CLIP)

GEN. DAVID PETRAEUS, COMMANDER, MULTI-NATIONAL FORCE-IRAQ: Recent operations in Basra, Mosul and now Sadr City have contributed significantly to the reduction in violence, and Prime Minister Maliki's government, the Iraqi security forces and the Iraqi people, in addition to our troopers, deserve considerable credit for the positive development since Ambassador Crocker and I testified a month-and-a-half ago.

(END VIDEO CLIP)

HUME: In other words, it seems things have gotten better there, not just due to the efforts of the U.S. military in Iraq, but due in these instances cited by General Petraeus today, to the efforts of the once seemingly feckless Iraqi government and Iraqi military.

Which does seem to indicate, Jeff, if General Petraeus is correct and news reports out of those areas indicate that he is, that the situation in Iraq could be very different, even more different come Election Day.

BIRNBAUM: Oh, yes. In fact, General Petraeus said that he expected to recommend further troop withdrawals come September, which I think we should take him at his word. In other words, there will be a declining number of U.S. soldiers in Iraq.

HUME: Below the surge line.

BIRNBAUM: Below the surge line, and possibly even getting toward the pre-surge line.

And this will be a very important plus for the Republicans and for John McCain. He will be running on the wisdom of his support of the surge policy, and against a completely different point of view from Barack Obama, who wants a timeline for withdrawal.

And if, in fact, things are getting much better, and noticeably better, and the violence is being reduced in Iraq, this could take one important issue away from the Democrats that they were really counting on.

HUME: Is it possible, Mara, that this issue could be a plus for the Republican nominee, or is that beyond hope for their point of view?

LIASSON: I don't think it's a plus. Look, if this trend line continues, this is a good thing for John McCain, as Jeff said. It proves he was right, especially as Petraeus said today, he could — he didn't rule it in or out — but he suggested he could remove a brigade — that's a lot of troops, 3,500.

But if things look good there, it makes pulling out also look more feasible. And, of course, that's what Obama wants to do.

HUME: But Obama wants to pull out regardless, whether it's getting better or not, right?

LIASSON: Yes. But I can't imagine this ever being a huge plus in the fall, unless we've got this functioning democratic government, and everything is wonderful.

HUME: That's milk and honey(ph).

LIASSON: But certainly having this trend continue is going to help John McCain.

KRAUTHAMMER: What's amazing is the emergence of the Iraqi state institutions, which everybody had sort of given up on. This is the Iraqi army on its own in Baghdad, the Iraqi army in Basra, which everyone had derided as useless, ineffective, defections, succeeds with some American and British help, driving the Mahdi Army, taking over the port, the most important economic asset in the country. It's also active in Mosul.

But what's so important here is that it is a Shiite government taking on Shiite extremists in Basra and Baghdad and succeeding. And, as a result, you get a domino effect where the leader of the parliament, the parliamentary speaker, who is a Sunni, who only a year ago spoke of the legitimacy of attacking American forces, writes a letter to the President of the United States effusively thanking him for the quality of the generals and the politicians he has in place.

Because the Sunnis understand that Maliki is acting as a national leader, acting against the Shiite extremists, and not only against the Sunnis. And the Sunnis have rejoined the government. And what you are having is the emergence of a reconciliation and of a state that's functioning.

HUME: Now if this, as Charles lays out, this perception takes hold, as well it might in the country, what is it going to sound like when you hear these calls that say the only way the Maliki government is going to get off its butt is if we threaten to withdraw and begin to do so. Will that ring hollow and sound untenable, or will that still remain popular?

BIRNBAUM: You won't hear that. It's not an argument anymore. I think some Democrats, of course, will continue to make the argument, but it will ring hollow.

Clearly, this latest report is very god news for the Bush administration and the Republican nominee, John McCain. In particular, and we need to emphasize here, Mosul, which had been the hotbed for al-Qaeda, has an 85 percent reduction in the amount of violence over the last recent term.

And I think if Petraeus can make the point that al-Qaeda is reducing its efforts in a major way in Iraq, that becomes even more of a plus for McCain.

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