Personally, I think the CW that Kerry should/will pick Edwards for VP is uncompelling and shows a poor understanding of how the VP choice matters.
The CW is driven by the phony notion of balance - the idea that the VP needs to balance out the P on issues, geography, etc.
I don't believe this because only insiders and partisans pay attention to the nuances of issue and style differences across the ticket. I think that swing voters who haven't decided which way to vote based on party consider the man at the top in 99% of their decision. A large portion of them don't even know who the Vice-President is, much less base their voting decision on him.
To me, the VP choice matters more because of what it says about the president, not because of the VP himself. For Bush, Cheney showed the adults would be running the show. For Clinton, Gore showed he wasn't going to be a captive to liberal special interests. For Bush I, Quayle told the conservative base he was with them.(1). Ticket balancing that plays to the center (Bentsen for Dukakis, Kemp for Dole) just doesn't seem to capture the attention of voters for whom it is supposed to matter.
Which brings us to Kerry. If he tries to appeal to conservative voters by picking Edwards, or Sam Nunn or whoever, it will play right into the hands of those who will label him weak, afraid to take a stand, wishy-washy, debate-club elitist, etc. Beyond that, conservatives will be able to play the out-of-step-with-our-values card all the more effectively by contrasting a southern Democrat's relative conservatism with Kerry's looney-left liberalism (which substance-wise with a guy like Edwards is baloney, but perception-wise, still holds water).
I think Kerry needs to show confidence and boldness with his choice. I'm going to steal a suggestion some people on this site made for Dean back when he was the nominee-apparent. I would like to see Kerry pick John Lewis from Georgia, an African-American congressmen, for his VP.
With Lewis on the ticket, they will be able to position themselves as being on the "right side of history" - Kerry outspoken against the Vietnam war, Lewis a civil rights activist. Kerry will also be able to say he is competing in the South with a Georgian/native Alabaman as his VP (in reality, he will be hard pressed to win there, probably, but that will be true regardless of who is on the ticket - if the Nascar demographic votes for Kerry it will be because of his Veteran status and eloquence, not because of his VP). Needless to say, this will also help Dems rally turnout among a core constituency nationwide.
Most importantly, this will show that Kerry is bold. Not afraid to take a stand, and not afriad to do what's right at political risk to himself. Beyond that, I think it will be able to insulate him from, not open him up to, attacks of lefty, out-of-touch, etc. When Republicans use that line of attack, he can castigate them for trying to divide us on ideology, on region, and on race, which is a hot-button attack that even most Republicans will steer away from (except in a few states we aren't going to win anyway).
Charlie Rangel from New York is another possibility. Bill Richardson from NM might also fit the bill. But whatever the case, I hope the Kerry campaign is thinking about the VP spot in these terms.
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(1) a history lesson you may not believe: Bush I used to be pro-choice.