If anything, it probably has a similar effect to LBJ's "we shall overcome", which was the main contributor to the Dem's loss of the great South. Dem has not recovered since than. But, in retrospect, desegregation contributed enormously to the advancement of American society. Imagine you and your kids have to sit in the back of a bus.
Let's see how Romney reacts. For him, it's a tricky issue too. He just can not be a bigot without the appearance of hypocracy. Not only the time of being bigot is over, he is also subjected to discriminition by evangelicals. To send the message, he'd have to invoke religion. Then, it will remind the evengelicals that he is not one of them.