Cain's base = Southern men:
More like "old southern men". And because the GOP folks are 95% white, "old white southern men".
Probably a form of white guilt. Former clan members and sympathisers in the 60s who now think: "Hey, we were once so mean to these black folks, but they are actually pretty cool and folksy and business-minded and they hate the Muslims, so let's make up for it and vote for one."
Meh, I'd say it's a bit reductive to say that all older white men in the South are "Former clan members and sympathisers".