I think you're making it more complicated than it really is. These people aren't that subtle.
Remember we're only really talking about the swing voters here -- the people who haven't made up their minds yet. They're the ones who pretty much decide every election these days.
And they tend to base their votes on feelings rather than rational considerations (like almost everybody does, actually). If they don't feel good about Obama, they're not going to vote for him.What could make them feel better than seeing him shake hands with every Christian hotshot in the country?
Which means it's a pretty brilliant strategy. So maybe he actually does have what it takes to be president...