In my view, the veepstakes frenzy currently descending upon us focuses on entirely the wrong set of questions. The debate is usually cast in terms of who can help win the election in November. I'll have more on this in a piece that will be on the website later this week, but the evidence indicates that running-mate selections usually have zero impact on election outcomes, even in the running mate's home state. (Recent polling data bear this out--Kansans are actually slightly less likely to vote for Obama if he puts Kathleen Sebelius on the ticket, and pairing him with Ed Rendell has seems to have basically no effect in Pennsylvania.) As long as you pick someone with a baseline level of competence and credibility and with no skeletons in his closet, you're probably not going to change things much, electorally. In the same vein, while there's an understandable desire on the part of pundits to see Jim Webb on the ticket because it would be, in Daniel Larison's words, "sociologically fun," in and of itself that's not a great reason to choose someone either.
But it also surprises me how little regard some people have for the vice presidency. I've heard people argue against Webb, Chris Dodd, and Evan Bayh on the grounds that their selection would jeopardize a safe Democratic Senate seat. This isn't a totally irrelevant consideration, but it should still be way down there on the priority list. There are a hundred senators, and seats change hands relatively frequently.
By contrast, a vice-presidential nominee is somebody who (in addition, of course, to being potentially a heartbeat away from the presidency) will instantly become one of the four or five most recognizable figures in the party, and will likely be a frontrunner for the presidential nomination at some point in the future. It's somebody who, with any luck, will be popular enough to campaign with and raise money for candidates across the country for years to come. And yet the conversation hardly focuses on this at all. One of the most important things a party does is cultivate talent for the future, and selecting a vice presidential nominee is absolutely critical in that regard. It's like deciding what to do with the top pick in the NFL Draft. Are you going to wind up with a Peyton Manning, or a Tim Couch? I can give you three reasons why the GOP presidential field was so weak this year: Dick Cheney, Jack Kemp, Dan Quayle.
Granted, there are other factors to consider--you want somebody who has a good working relationship with the presidential nominee, and preferably someone who can help take the lead in shaping policy in a few key areas of expertise. (Ideally, of course, not someone who will wind up effectively running the entire federal government.) But far and away the most important question is: Is this somebody you want closely identified with your party brand for the next two decades? Anyone trying to make the case for selecting a particular running mate should be prepared to explain why the party will benefit if that person becomes, overnight, one of its biggest names.
I'm not totally opposed to the idea of an Obama–Clinton ticket, but this strikes me as one of the main arguments against it. Hillary is already a major figure on the national stage; she will continue to be very influential regardless of whether she's the veep nominee. There is no shortage of promising prospects who could achieve much if given that level of stature--why pass up the opportunity to put one of your rising stars in that position?