"I think he's going to make an intensely political choice, not a governing choice," Rove said. "He's going to view this through the prism of a candidate, not through the prism of president; that is to say, he's going to pick somebody that he thinks will on the margin help him in a state like Indiana or Missouri or Virginia. He's not going to be thinking big and broad about the responsibilities of president."
Rove singled out Virginia governor Tim Kaine, also a Face The Nation guest, as an example of such a pick.
"With all due respect again to Governor Kaine, he's been a governor for three years, he's been able but undistinguished," Rove said. "I don't think people could really name a big, important thing that he's done. He was mayor of the 105th largest city in America."
Rove continued: "So if he were to pick Governor Kaine, it would be an intensely political choice where he said, `You know what? I'm really not, first and foremost, concerned with, is this person capable of being president of the United States? What I'm concerned about is, can he bring me the electoral votes of the state of Virginia, the 13 electoral votes in Virginia?'"
Kaine, who is widely seen as one leading contenders to become Obama's running mate, said that the fact that Obama is competitive in his home state of Virginia is "basically astounding" since no Democrat has won there since 1964.
He said polls that show Obama with only a slight edge over rival John McCain nationally are not a cause for concern.
"We are feeling very, very good about where the senator is in the polls and we obviously expect as America - the American electorate turns their attentions even more to this race in connection with the conventions, we expect to do - to do quite well," Kaine said.
Kaine suggested that McCain's recent ads casting Obama as a celebrity are "out of touch with what the issues are."
"I mean, it was funny, but wearing a clown suit and juggling would be funny, too, but it doesn't connect with the concerns Americans have about gas prices, about the war, about the economy," he said. "So I think on things like that, shoot, I hope the McCain camp does more of those ads and we'll just let them do those ads."
He added that while Obama is running positive ads during the Olympics, "Senator McCain is running the same old negative, Karl Rove-style ads that we're all tired of."
Rove said the closeness in the polls between McCain and Obama is a signal that Americans are have concerns about the Illinois senator.
"With a restive electorate, with an economy that's sort of chugging along, with a war in the background, at the end of eight years of Republican rule in the White House, Obama should be way ahead," Rove said. "...the fact that he isn't says that there are grave doubts about Senator Obama."
Rove said Kaine's characterization of McCain's ads compared to Obama's was wrong.
"I would make the argument that part of the reason why Senator Obama is in the shape he is in today is because he's failed to run a positive campaign," said Rove. "He's run a negative campaign. He's claimed to be something new and different, and yet given these - you know, it is really beyond the pale to sit there and insinuate that Senator McCain is somehow going to attack him for being black, which is what he did for over a month."
Read the full "Face the Nation" transcript here.