I think you're over-estimating the common Palin supporter. Most of her supporters would say they "like" her as their reason for supporting her, whatever that means. My guess is it means they think if they knew her personally they would be friends with her judging from her choice of words and seemingly similar political views, but people believe lying, corrupt politicians all the time that would befriend them and stab them in the back. So liking a politician is a pretty ignorant thing to do without being very informed about them.
I'm just pointing out I don't think Palin supporters have a substantial reason for supporting her. She doesn't even say anything substantial. She's as vague as you can possibly be. Its amazing how much Palin talks, but how little she truly says at the same time.
So while I agree we need to get them to wake up and start thinking, instead of just deciding to like someone, I don't see how to do it really. Or at least not in a way specific to Palin supporters. There's a female appeal there, but the only way I can think to exploit that is to convince them Ron Paul is a woman, and it just might be possible with Palin supporters...