Whites did not 'get more Republican overall'. Rich whites did get more Republican, while working-class whites actually got substantially more Democratic, especially in parts of North Jersey. The result was probably a wash in terms of white voters across the whole state.
As for barfbag's comment, by mid-October, Romney had stopped gaining, and after then he steadily lost pretty much everything he gained. The hurricane simply accelerated this process. Even if not for Sandy, Obama would still have won New Jersey with at least 55-56 percent of the vote.
Hudson County's swing can also be attributed to the massive swing toward Obama among Cubans. While the Hudson Cubans were always more Democratic than the Miami Cubans, the Hudson Cubans still swung heavily toward Obama.
Early-mid October is when Romney began to gain.