Roger Simon at the Politico says no, but goes through a lot of reasons why Hillary Clinton might select Barack Obama as her running mate once she wins the nomination. Simon mentions the need for unity after a fractious primary, Obama's draw among black voters, and his organizational skills. Simon waits until the concluding paragraphs to give what he sees as the countervailing argument (via Memeorandum):
So why wouldn’t Hillary put Obama on the ticket?
There are two unbreakable rules for picking a running mate: Never pick anybody who might overshadow the top of the ticket, and never pick anybody you cannot completely control.
So Obama might be eliminated on both counts.
Then there is the Rule of Firsts. The Clinton campaign does not want to force too many “firsts” on the American electorate.
Electing the first woman president will be challenge enough. Electing the first woman president and first African-American vice president at the same time? Forget it; they don’t need that kind of problem. (The same reasoning might prevent New Mexico Gov. Bill Richardson, who is Hispanic, from getting the vice presidential nod.)
I don't find either argument compelling. The Rule of Firsts must have been passed just recently, as it has never been an issue before this electoral cycle. The only first that either party has offered in the last couple of generations has been the nomination of Geraldine Ferraro as the running mate to Walter Mondale in 1984. Mondale didn't exactly represent a complete break from history in Democratic nominees; he was a former VP and long-time Senator.
Simon's argument about control doesn't make much sense, either. Barack Obama hasn't exhibited any noteworthy variations from the party line, except in his insistence that he runs a different kind of campaign. Simon's suggestions actually get much worse, especially in his inclusion of Jim Webb, an infamous loose cannon. Evan Bayh has his own strong constituency and family tradition, and would be much less malleable by the Clintons than the first-term Obama. Even Dan Quayle had more seasoning than Obama.
There is one good argument for Obama as VP, and two good arguments against it. Obama has built an organization that rivals Hillary's, and combined they could be tremendously effective in the general election. The two arguments against Obama are really one with two parts. Obama adds nothing in terms of votes to the ticket. Hillary will carry Illinois with not much difficulty, given the Republican disarray there, and she'll carry the black vote 9-1 regardless of running mate. Obama won't help in the South; Simon seems to forget he doesn't come from there.
I'd expect to see either Tom Vilsack or Bill Richardson as the VP. She needs regional balance that both men can provide, and she needs executive experience on the ticket that she lacks. Obama can't provide either of those qualities.