All the reports I have seen state that VP picks don't actually bring a state on board. Look at Portmann as a case study. The difference with him and Biden added to the polling is nothing. Obama won Ohio in a questionnaire whether Portmann was on the ticket or it was straight between Romney and Obama. The change was one percent and had no effect on the outcome at all.
Yeah I dont see nominating a VP purely in hopes of getting a swing state(or increase a greater appeal to get a few swing states).
I may be going outside of the box on this pick...but what about the cat helicopter for VP? I believe his name is Orville