It may well extend beyond that, including lower Manhattan, Queens and Long Island. Here is the county results map from the 2004 presidential campaign (Bush vs Kerry). Blue=Bush; Red=Kerry
The majority of New Yorkers voted for Bush but Kerry won the state with the large metropolises. New York is still considered Obama country but, between the carnage in Queens, the long gas lines, the power outages and the slow response from FEMA, I'm betting that a lot of hungry, unbathed residents who have lost their homes or been displaced by water damage, may very well pull the lever for Romney.
More likely, they just won't vote at all - which is still a win for Romney. Not nearly enough to flip the state, though.