Obama picks Hagel as veep?

This will be very important for a story I'm thinking of writing.

Prior to the election, there was substantial speculation that Obama might pick Hagel: see, for example, here, here, here, and here. Unlike a speculative McCain-Lieberman ticket, base enthusiasm wouldn't have been a problem; if anything, Obama suffered from a surfeit of enthusiasm. How could such a ticket have resolved obvious differences of ideology? Could it have tossed the election to McCain-Palin, or increased Obama's victory margin? And how would such a ticket govern?
 
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