Concerns were raised that voters in New York City and the surrounding areas would not be able to make it to polling stations after the superstorm rendered voting centres useless.
Officials in New Jersey say people displaced by the storm will be allowed to vote by email, and in New York 143,000 people will be assigned new polling stations. Both states are usually easy wins for the Democrats.
Close to two million people are still without power after the storm battered the US coast a week ago.
Schools in New York were expected to re-open today, but between 30,000 to 40,000 people are in need of shelter.
Around 1.9 million homes are without power in New York and New Jersey, and the pressure is on utilities companies to restore networks ahead of a storm expected midweek which will bring with it freezing temperatures.