I think so. Most of his problems with the base are over his behavior, not necessarily actions he's taken as Governor, and could be washed away once he starts campaigning as a conservative Republican.
Do you really think his Tea-Party opponents (for the sake of argument, let's suppose Rand Paul runs) will let the base forget Chris Christie's transgressions against GOP orthodoxy -and worse, his (sometimes even physical) closeness to President Obama? I think you underestimate the potency of the argument offered by the true believers that the GOP has tried going 'moderate' the last couple of times -and both times they lost. And they will not hesitate to point out that McCain and Romney lost because they weren't right-wing enough, that now is a time to nominate one of their own, a man (or woman) of spotless adherence to conservative principles.
Judging by what has happened to Marco Rubio's 2016 chances (regardless of the fate of immigration reform in Congress), I would not hold out hope that the saner elements of the GOP will win out yet again with Chris Christie as your nominee.
The thing is though that in order for the primaries to produce a Tea Part nominee, the conservatives will have to unite behind a single candidate. In a field that could potentially have Rubio, Paul, Santorum, Walker, Cruz, Perry, and possibly others, I'm just not sure that'll happen. All while Christie will have the moderates and indepedents to himself.
I'm not denying that he'll have problems, but again, I just don't see how Christie's transgressions against GOP orthodoxy are anyworse than those of McCain or Romney. Especially since with his, he has a pretty simple defense of why should his constituents have had to suffer for political reasons. Which seems pretty sound when compared with Romney trying to explain Romneycare as a states right issue.