The following is a partial transcript of the July 27, 2008, edition of "FOX News Sunday With Chris Wallace":

"FOX NEWS SUNDAY" HOST CHRIS WALLACE: For a different perspective on Obama's world tour and where the campaign stands now, we turn to the man behind two presidential election victories, FOX News analyst Karl Rove, who joins us from Nashville.

And, Karl, welcome back.

KARL ROVE: Good morning.

WALLACE: First of all, your overview of Obama's trip — did he shore up his credibility as a potential president and commander in chief?

ROVE: I think the short answer to that is we don't know. Every big event like this has plusses and minuses. And there are some things that he did that did shore up his standing.

For example, he was on the same world — he was on the same stage with world leaders. There was the shot of him in the helicopter with Petraeus over Baghdad in the stories. And he clearly dominated the media with his world tour for, you know, more than a week.

He received a semi-endorsement from Maliki of this idea that U.S. troops could be brought out by the — by 2010, though there is a big difference, I think, underneath the surface between Obama's view and Maliki's view.

And finally, he had these huge crowds in Germany. And those were all on the plus side, and that helped him.

On the other hand, he remains against the policy — the surge — that made success in Iraq possible, and I think that's hard to fathom. The dominant photograph of the opening stage of this world tour was him hitting a three-point shot in Afghanistan. I'm not certain that's the best image if you want to say, "I'm a world leader."

He had three tough interviews with Terry Moran, Katie Couric, Gibson — they were all tough interviews. And the crowd was big, but it was in Germany, and he's running for president of the United States, not president of Europe.

And then finally, we had this dust-up over the visit to wounded troops, and there was also sort of a hint of arrogance. They demanded that they be — that he be treated as a — as the occupant of the White House, with White House rules.

And I think, frankly, finally, the speech in Germany, while it was soaring in its rhetoric, was actually, you know, somewhat vacuous. I mean, I'm not certain there was much "there" there. And he's received some criticism in the European press for it.

So on balance, I think, short-term plus, but potentially a long- term — long-term, it might not make that big a difference for him.

WALLACE: I want to go back to the — particularly the reception from the Europeans and that extraordinary crowd in Berlin — 200,000, according to police reports.

Back in 2004, you and other Republicans went after John Kerry as being too continental, too European, in his sensibility. I talked to the Obama camp about that this week, and one of the top strategists said to me that they feel the country is way past 2004 and freedom fries and now would very much welcome European support.

Do you think playing well on the European stage helps or hurts Obama back here at home?

ROVE: You know, look. I don't — I think they're misreading it. It worked in 2004 because John Kerry's sensibilities were so, you know, Francophile. I mean, you know, he was a European elitist.

Obama doesn't look that way. And frankly, though, going to Europe and putting the emphasis on this big crowd and the big event in Germany, and the dust-up, and "I want to speak at the same place that President Ronald Reagan and President John Kennedy spoke," I think that all had a note of disquietude to it.

It bespoke a little bit of arrogance and brashness, you know, sort of like, "I want the privilege that presidents had." But I don't think — look. Americans like that their foreign — that their leaders are liked by foreigners.

But more important to them than that is what do their leaders stand for. And you know, in 2004, Kerry was the stereotype — I don't think Obama fits the stereotype yet — of a — you know, sort of a European-oriented American leader.

WALLACE: Let's talk about the practical political impact here at home. Some people thought with all of this massive coverage and some pretty powerful visual imagery that there would be a bump in the polls, but the early indications are that he hasn't gotten much of a bump nationally.

And I want you to take a look at these Quinnipiac swing state polls. In Colorado in the last month, Colorado has gone from Obama up five to McCain up two, Michigan from Obama plus six to plus four, Minnesota from Obama up 17 to up two, and Wisconsin from a 13-point Obama lead to an 11-point lead.

Why do you think, Karl, that both in swing states and nationally voters are not ready to jump aboard the Obama bandwagon, even despite all of this burst of publicity?

ROVE: Yeah. You caught a very interesting secular decline for Obama since roughly mid-June. In RealClearPolitics.com, it's down to a 4.8 percent race. And in the FiveThirtyEight.com tracking number, it's down to a two-point race.

I think there are three things here. One is the doubts about Obama's experience and fitness for the job. In March, I believe it was, ABC-Washington Post poll said 46 percent of the American people believe that he lacked the experience to be president.

He then spent $119 million between March and the end of June on his campaign, including a lot of advertising in key states, and at the end of June, Washington Post-ABC asked the same question again and the dial hadn't changed. Forty-six percent said that he lacked the experience and qualification to be president.

You normally find both candidates somewhere in the 60 percent to percent range on that question. Here's a guy who can't even bump 50 percent.

Second, McCain has strength among independents. In the FOX poll, independents are essentially split, 32 McCain, 34 for Obama and 34 undecided.

And there is resistance — contrary to what Senator McCaskill said, there is resistance among Clinton Democrats. If you take again a look at the FOX poll, 86 percent of Republicans are for McCain. Only 75 percent of Democrats are for Obama.

Twenty-five percent of Democrats are either for McCain or undecided. That's a pretty big number to have at this point in the campaign.

WALLACE: I want to ask you about another thing that we saw in those Quinnipiac swing state polls. They found that there's one issue that is beginning to cut strongly for Republicans, and that is energy. By margins...

ROVE: Energy.

WALLACE: ... of 20 points to 30 points, voters are now saying that they support offshore drilling. How much could that help...

ROVE: Right.

WALLACE: ... McCain and hurt Obama?

ROVE: I think it's driving a big number for him, particularly among working-class blue-collar Democrats. Again, this is one of these interesting things. I wrote about this this week in the Wall Street Journal.

Look, every political candidate changes their mind. The key question is do you admit you changed your mind, did you share the new information that caused you to change your mind, and does it seem authentic, not calculating.

And John McCain reversed himself on drilling on offshore — on the outer continental shelf and developing the oil shale in the Rocky Mountain states, and he said, "Look, $4-a-gallon gas has caused me to change my position."

Well, a lot of Americans, according to the polling data, have over the last several years, and particularly this year, begun to change their attitudes about expanded drilling off of our coasts and the development of the oil shale. And again, it's the same reason — $4 a gallon gas.

So we have an emerging dialogue here, a difference on energy. We have McCain saying, "Drill more, use coal, expand alternatives — wind, solar and exotics — and let's conserve more and build more nuclear plants," and you have Obama saying, "Well, I agree with you about the alternatives, and I agree with you about conservation, but I'm against drilling more, I'm against nuclear plants, I want to tax coal, I want to tax natural gas, and I'm really down on developing any more additional coal-powered plants."

So you know, we've got a dialogue here that could end up working to McCain's advantage in a pretty powerful way.

WALLACE: Karl, let's look at the latest Rove electoral map. And what's interesting about this is that two weeks ago, you had Obama with 296 electoral votes, 270 needed to win the presidency.

And now, two weeks later, you have Obama dropping to 263 electoral votes. McCain hasn't picked up, but the toss-ups have. What's going on there?

ROVE: Right. Well, Ohio and New Hampshire had moved from Obama to toss-up, and Nevada has moved from McCain to toss-up. I suspect there's even more going on.

You mentioned the Quinnipiac polls. Those are going to begin to be seen in this rolling average of polls, so we're likely see even more of these states close up.

We have the largest number of toss-up states, 83 electoral votes, since we've had in April. And again, I think this is a result of — you saw the national polls begin to show a tightening. And the state polls, which are not done as consistently or as often, are going to tend to reflect that, and we're starting to see that show up.

I wouldn't be surprised if next week we didn't see Obama drop below 270 and McCain actually begin to add some numbers to his total.

WALLACE: We've got less than two minutes left, and I want to go through the vice presidential issue with you.

First of all, timing. There were reports this week that McCain was going to name his vice presidential running mate this week to step on the Obama story. Obviously, that didn't turn out to be true.

Now there are stories that he'll name him or her before the Olympics. If you were running the McCain campaign, just from a timing standpoint, when would you tell him he should name his running mate?

ROVE: I would wait until after Obama named his, because I'd want to keep that pizzazz and that — even if that meant I had to do it during the week of the Republican Convention.

And interestingly enough, the key determinant here in announcing the vice president is going to be Obama's choice of a vacation date, in my opinion. He's not going to name his nominee before he takes the week off that we understand he told the Tory Party leader in Britain that he was going to take off.

So I think that we're going to have to wait until he has his vacation. I wouldn't be surprised to see him come back off of his vacation and name the nominee. I would suspect it's likely to be close to the beginning of the week of the 18th, either late the week before or during the week of the 18th.

But I think if I were McCain, I'd wait until after the Democrats chose theirs, even if it meant I waited until the week of the Republican convention.

WALLACE: And just real briefly, your sense — give me two names that you think at this point are the leaders on the Republican side and on the Democratic side.

ROVE: Well, Mitt Romney on the Republican side. We had a buzz last week for Pawlenty. I don't know if this was deliberate on the part of the McCain campaign or just the accidental, you know, conversation that we have.

And on the Democratic side, you know, I don't know. I think you had one of the key possibilities on your show just a few moments ago. I think McCain — or Obama is going to be looking at a red state Democrat — Claire McCaskill coming from a Republican-oriented state where — I was just there yesterday or day before yesterday, and they're feeling pretty good, the Republicans are, about keeping Missouri in their column.

But McCaskill might be a way for Obama to try and get at the heart of this battleground state.

WALLACE: Karl, thank you. It's always a pleasure. And we'll talk to you soon.

ROVE: Thanks, Chris. Great.