After receiving reports from the state's 21 counties, Gov. Christie said Friday that it appeared only 10 polling places statewide would be entirely inaccessible Tuesday.
Officials did not say how many other sites might be affected by other problems, such as loss of power.
In some cases, the governor said, voters will go to their usual polling locations to find trucks or trailers where they can vote "old school" by paper ballot.
"Everybody in New Jersey will have a way to vote," he said. "It will probably take us longer to count the votes, but it will be a late night anyway."
As for voters who have relocated far from their home counties and do not plan to return by Tuesday, they are out of luck, unless they have posted mail-in ballots.
For those who have remained close to home but are not sure they can make it to their polling stations on Tuesday, the question will be whether they are willing or able to make a special trip to their county election offices during the weekend or on Monday.
And while efforts are under way to ensure voters get a chance to cast a ballot, there is one unknown: Were any mail-in ballots destroyed when Sandy's waters flooded Postal Service boxes?
The obstacles to voting thrown up by nature and the breakdown of the electrical system come as the Gallup polling organization said its pre-Sandy surveys indicated that turnout nationwide this year would be below the 57 percent and 58 percent recorded in 2004 and 2008, respectively.
Richard Harris, chairman of the political science department at Rutgers-Camden, said the storm's impact "makes things difficult" for voters but probably won't change where New Jersey "comes out on the electoral map."
"New Jersey is so blue, it is unlikely a decline in turnout would flip it to a red state," he said.
That means President Obama likely will carry the state.
Harris said there is one caveat. The urban counties of Hudson and Essex - Democratic strongholds - were among the hardest hit and low turnouts there "will depress the margin of Democratic victory."
He said that also applied to the only statewide race on the ballot, the U.S. Senate race between Democratic incumbent Robert Menendez and GOP challenger Joseph Kyrillos.
Harder to gauge, however, will be the effect on local races in hard-hit areas.
In a directive issued Thursday, Lt. Gov. Kim Guadagno instructed all county clerks and election offices to open at least between 8:30 a.m. and 4:30 p.m. on Saturday, Sunday, and Monday to enable registered voters to cast paper ballots.
In Ocean County, which includes Long Beach Island and Seaside Heights, officials announced that voters could obtain paper ballots at a second location besides the county seat in Toms River.
Registered voters from the six communities on Long Beach Island, as well as the municipalities of Barnegat, Eagleswood, Lacey, Little Egg Harbor, Ocean, Stafford, and Tuckerton were urged to visit the county's Southern Service Center at 179 S. Main St. in Stafford.
In Atlantic and Cape May Counties, voters seeking to cast a paper ballot in advance of Tuesday's election must go to their county seats in Mays Landing and Cape May Courthouse, respectively.
Election officials in Camden, Burlington, and Gloucester Counties said they expected to have all their polling stations operating Tuesday at their usual sites, or close by.
Still, their county clerk and election offices will be open over the weekend to provide paper ballots.
Contact Joseph Gambardello at 856-779-3844 or firstname.lastname@example.org.
Staff writer Amy Rosenberg contributed to this article.