...is all about confirmation bias. Our brains seem hardwired to win arguments rather than find the truth. So when the appropriate sound bite comes along it doesn't even matter if it's true as long as it's what people want to hear. I think this is where litmus issues fall. Once the politicians get all their ducks in a row they can do whatever they want.
Dirty politics is about this bias. There's a famous story about LBJ talking to staffers about spreading a lie concerning his opponent. When they objected because it just wasn't true, he replied "I just want to hear him say he doesn't f**k pigs". Images like that will linger longer than any policy statement.