As a practical matter: when dishonest political marketing can convince voters it does, as with John Jerry's vote on war funding.
My answer: when the reason for the flip-flop is not based on new information or reasonable development of judgement, but on self-interest implying dishonesty in the original reasons given for the position.
Consider, for example, Bush's outrage expressed at the Plame outing initially. With the nation largely angrey about it, his own father having a quote about how horrible it is for someone to out a CIA agent, and what seemed like a very low risk of getting caught, he did what was politically beneficial and easy, and hopped on the bandwagon to attack the outing, making promises he didn't expect to be held to.
He gambled, and lost. When it was confirmed his top people were responsible, rather than 'who knows who in the thousands in many agencies', he blatantly reversed position and refused comment.
Another example would be his switch from being extremely dedicated to catching Osama bin Laden when politically helpful, to 'doesn't think about him much' when he wasn't catching him.