County election officials could ask the New York state Board of Elections to allow polls to reopen for another day if the turnout on Tuesday is less than 25 per cent, state board spokesman Thomas Connolly said.
"To my knowledge this has never happened in New York," Connolly said. "Will the turnout be low? It's hard to say -- probably, it all depends if people have other priorities."
The state board would consider the request and, if approved, a second day of voting would be scheduled, he was quoted as saying by CNN.
Polls would be open for 11 hours on the second day, with only those who were eligible to vote on Tuesday allowed to cast ballots.
Nassau county elections commissioner William Biamonte said he expects a "significant drop off" in the turnout of Long Island voters.
"A lot of people that are displaced ... they're worried about getting their lives back, and whether they're going to go back to an area where they've lost power, or their home has been lost, rather than take care of what their immediate needs are, that's a big question," Biamonte said.
Getting polling sites ready has been a "slow, tortuous process" since Sandy hit the county, he said.
Election officials relocated and consolidated 40 polling sites, while another 30 will be powered by portable generators, he said.
The New York City Board of Elections has decided to temporarily relocate or combine some polling locations across all five boroughs serving 143,000 voters because of damage from Sandy, New York Mayor Michael Bloomberg said on Sunday.
Bloomberg, who called the election board "dysfunctional," said he was concerned about polls being opened on time on Tuesday and poll workers and voters knowing where to go.
"The difficulties they've had in planning for Tuesday further underscores that," he said.
New York City officials on Sunday said that they faced the daunting challenge of finding homes for as many as 40,000 people who were left homeless after the devastation of last week's storm.
The number of customers without power in New York was over 1.8 million, the energy department said.