Your argument somewhat undermines your point. Santorum, Perry, Bachman...none won the primary. It was the Mormon moderate from the Northeast who won. Not exactly the poster boy for the ultra conservative christian right of the republican party.
Yes, he did have to move to the right to win the primary. Just like McCain had to. I agree with you there. And, I can agree that Christie will have to appeal to that base if he runs in '16 to try and win the nomination. But, I still like his chances more than you're making it out to be. You act like it's an impossibility.
First, we have no idea how much influence the tea party will have in '16. Secondly, not everyone who votes in the republican primary is a card carrying member of the tea party. Most who vote in the primary are pragmatic. They understand that of the however many people running for president in their party, there are probably only two or three realistic chances of guys actually becoming president. Christie is absolutely one of those guys. He'll get plenty of votes from people who may not love him, but know this guy has a chance of winning a national election. Again, look no further than Romney's nomination.