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(CNN) -- Long, slow-moving lines stretched around polling stations across New York City a week after Superstorm Sandy's fury threatened to keep many citizens from voting.
"It's inspiring to see so many people up and out to vote already," said one woman at a makeshift polling station in Brooklyn established to replace regular precinct locations made unusable by storm damage.
While inspiring to some, the long wait to cast a ballot was frustrating for others.
Gov. Andrew Cuomo's last-minute decree that any voter could vote at any precinct, intended to help those displaced by Sandy, made it "a little insane right now" at the polling station at Public School 41 in Greenwich Village, a poll coordinator there told CNN Tuesday afternoon.
"So we have everybody coming in from everywhere," said the coordinator, a Republican who asked not to be named. "It was for displaced people, but others are taking advantage of it."
The affidavit ballots these people cast take longer to process, she said.
Another reason for slower voting is that the city adopted a new system of machines that scan paper ballots, replacing the levers of the old-style voting machines, she said. Voters must stand in two lines now: One for filling out the ballot and a second for scanning it.
"Today is an interesting day," New York City Elections Commissioner J.C. Polanco said.
In some cases, three or four voting sites were consolidated into one location because of Sandy damage, Polanco said. That means 3,000 or 4,000 voters potentially standing in the line instead of just 1,000, he said.
"We'd ask the patience and tolerance of New Yorkers," Cuomo said during an afternoon news conference. "This is a critical election. I believe this country, this state, has many important issues it's facing. Whatever your preference today, please vote and exercise your right."
The New York City Board of Elections temporarily relocated or combined some polling locations serving 143,000 voters across all five boroughs because of damage from Sandy.
New York City Mayor Michael Bloomberg said late deliveries of polling equipment occurred in some areas and at least one site did not have enough gas to keep electric generators going.
"I know many people are encountering long lines at the polls," he said. "Be patient. It's part of the process."
At one temporary polling station inside a Brooklyn school, which was also used as a shelter for residents displaced by last week's storm, one man said the long line was too much for him Tuesday morning.
"I've got time in the afternoon, but right now I don't," he told CNN. "But I'll be back to make the wait."
Voters in some New York counties could get an extra day to cast ballots if disruptions caused by Sandy prevent enough citizens from showing up at the polls, a state official said Sunday.
County election officials could ask the state Board of Elections to allow polling places to reopen for another day if Tuesday's turnout is less than 25%, according to board spokesman Thomas Connolly.
The state board would consider the request and, if approved, a second day of voting would be scheduled within 20 days of Tuesday, he said.
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.
CNN's Josh Levs, Chris Boyette and Alina Cho contributed to this report.