I think the biggest issue in the backlash against her is that she handled this very badly. Her apologies came off very staged, none of them sounded sincere, and her appearance on the Today show was more her feeling sorry for herself than for what she did. My honest take on this situation is that she really doesn't clearly understand that her behavior was offensive. She seems to think she is just a good ol' Southern gal an she should be excused for acting like this.
Personally, I don't feel the least bit sorry for her. As a doctor, she pissed me off with her "oh, now that I have a huge endorsement I'll come out as a diabetic and go all healthy" on people, and based on the data I've seen, I think she considers minorities to be inferior. She did this to herself and when it all broke, she completely mishandled the situation. She hasn't made a truly sincere mea culpa yet. She made her own bed, time to lie in it and deal with the fallout.