As several people have pointed out, the "home state advantage" doesn't automatically flip a state from one party to the other, but it is likely to shift the overall vote by some portion. To take a realistic example, Minnesota leans slightly Democratic in presidential elections. Tim Pawlenty is a potential Republican candidate for president in 2012 and is currently the governor of Minnesota. There are certainly plenty of people in Minnesota that are sticking with their party affiliations regardless of who is on the ballot, but there are likely to be some people towards the middle that could be swayed somewhat by the potential added benefit of a person with particular loyalties to their state now occupying the White House. Now, Obama won Minnesota by 10 points, though it's reasonable to argue that 2008 was a Democratic "wave year." If the political climate is substantially different in 2012, a generic Democrat might be something more like a 4-point favorite against a generic Republican. Thus, if Pawlenty was the nominee and was able to swing his home state by more than 4 points, he would end up swinging the extra 10 electoral votes towards the total of 270 needed to win the presidency. On the other hand Giuliani was a potential 2008 presidential contender from the state of New York. I don't have the exact numbers, but I think Democrats usually win New York by about 20 points or so. Even if the home state advantage accounts for a swing as large as 10 points, if Giuliani had been the nominee, he still wouldn't have won New York (even in a non wave year), even though the vote would have been a good bit closer.
One of the best electoral statisticians I've come across is Nate Silver from
http://www.fivethirtyeight.com. I went digging through his site again to see if I could find exact numbers on what the swing actually is. I recall seeing him talk about it a couple times, but the first specific mention I could find in a few minutes of searching was a
7-point swing. However, that's for the president.
The vice president doesn't usually offer that much of a swing.