Turns out not to be so
I was catching up on The Mentalist, and caught the tag end of a The Good Wife episode. Some woman was telling Chris Noth's character that he should quit his campaign and be her running mate. She said she had plenty of her own money and she could afford to spend lots. "People are attracted to someone who's willing to spend their own money," she said.
Well, I have no idea how it's playing out on that show (despite liking the actors, I really disliked the first three or four episodes and haven't watched it since). But in real life we've seen just the opposite. Plenty of people ran this last time, and the time before, spending a lot of their own money (like Carly Fiorina, Meg Whitman, and Linda McMahon, for example). And they weren't attractive enough to enough people.