First, there's dismissing the story as no big deal. Whether that's true or not is a subjective judgment. But if your cronies really did massively inconvenience a whole city as part of a political payback that actually is a pretty big deal - and one that raises specific vulnerabilities for Christie and he tries to move on to the national stage.
Second, don't make false statements that are actually secondary to the story itself. If he ordered his friends to do this (something for which there's no direct evidence and I can't imagine it went down that way) then, okay, maybe he just has to deny that. But saying that Fort Lee officials didn't say anything about the traffic jams at the time seems easily refutable. Why burn through credibility on something like that, especially since it's not clear that complaints like this would make their way up to the governor's office.
I suspect the answer is that Christie is just Christie. He's aggressive, doesn't like being questioned and doesn't self-censor. That's mainly why he's popular after all. But in this case, it doesn't serve him well at all.
As I've said before, I think this story is potentially quite damaging for Christie. How damaging a scandal is for a politician is never wholly a matter of the nature of the alleged wrongdoing itself. It's far more about how the behavior confirms negative perceptions or damages positive ones. There are two problems with this for Christie. One thing is that New Jersey politics is just intrinsically weird and crooked. This is pretty ballsy even for New Jersey. But in the rest of the country, I think people see something like this and think, "What? You're kidding."
It just seems thuggish and sort of nuts. And that's already the sort of bullyish, poor anger management image that is Christie's biggest liability. No, I don't think this brings him down. But I suspect it tarnishes him going into 2016 and gives his critics a perennial point to hammer on and one he has difficulty responding to in any effective way.