Still reeling from superstorm Sandy and bracing for more rough weather, voters in New York and New Jersey faced confusion and long lines Tuesday as they cast ballots in a variety of established and makeshift polling places, including tents set up to serve displaced residents and a tricked-out Winnebago.

With more than 1 million homes and businesses still without power eight days after Sandy’s onslaught, and with polling stations among the thousands of buildings damaged, voting in the storm-ravaged states involved unaccustomed challenges. The governors of New York and New Jersey invoked extraordinary measures to ensure that people would be able to participate, and many voters welcomed the opportunity to exercise a right that they previously took for granted.

New York Gov. Andrew M. Cuomo (D) issued an executive order allowing displaced residents to vote by provisional ballot at any polling place in the state for president and statewide office holders.

“We want everyone to vote,” he said. “Just because you are displaced doesn’t mean you should be disenfranchised.”

New Jersey Gov. Chris Christie (R) ordered election authorities to allow displaced citizens to apply for a ballot by e-mail or fax. But the state quickly became swamped with requests, and many voters complained that they did not receive a ballot back or could not reach election clerks’ offices. Officials later said some voters may not receive e-mailed ballots until Nov. 9.

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Christie nevertheless insisted that the voting was running smoothly.

“Of our 3,000 polling places across the state, less than 100 were compromised and had to be moved,” Christie said, according to the Newark Star-Ledger. “Everyone should find the time to vote today, but the only people who should be applying for their ballots online are voters affected by the storm. Everyone else, get your butt up and go to your polling place like normal.”

Faced with a nor’easter that is forecast to strike Wednesday, bringing another round of coastal flooding to the Mid-Atlantic and southern New England, New Jersey’s Brick Township issued mandatory evacuation orders for residents in low-lying waterfront areas by 6 p.m. Tuesday. The new storm is expected to pack heavy rains, wind gusts of up to 60 mph and a tidal surge of three to four feet above normal in some areas.

Hurricane Sandy killed 69 people in the Caribbean before colliding with a nor’easter as it struck the New Jersey coast on Oct. 29. The resulting superstorm killed an additional 113 people in the United States and Canada, knocked out power to 8.5 million homes and businesses, devastated seaside communities and flooded New York City’s streets, tunnels and subways.

In some polling stations in New York, the introduction of new digital voting equipment created more of a headache than the storm.

At the Brooklyn Museum, which was largely untouched by Sandy, voters had to wade through a complex tangle of lines to obtain a ballot. Three of the station’s four scanning machines failed, adding an extra hour to the wait.

“It is just a nightmare,” said New York City Mayor Michael R. Bloomberg (I), who encountered a similar problem at his voting station.

Bloomberg said that New York’s old manual voting system was far simpler, requiring voters to enter a private booth and pull a long crank to register their choices. The current system, he noted, requires voters to wait in line to obtain a card and a ballot in a manila folder, then go to open voting booths with no privacy, and then wait in another line to have their ballots scanned.

“What’s this, a third-world country,” he overheard another voter saying.

In some storm-struck areas, the voting went off without a hitch. In Sheepshead Bay, Brooklyn, the voting station at Bay Academy public school, which had been badly flooded by Sandy’s storm surge, was up and running early Tuesday morning.

“I had no problem whatsoever,” said Charles Cognata, 72. “It was more organized than the last time I voted. I would have liked to stay longer. It was nice and warm in the school. I haven’t had heat for the last week.”

But others were unsure whether they wanted to vote.

“I haven’t decided if I’m going to attempt to go to vote,” said Barry Weinstein, 61, of Sheepshead Bay. He said a lackluster local response to the flooding in his community had put him off politicians. “What’s the point? If I go to vote, I’ll vote for president. Anyone else in my community, you know where they can go.”

Maggie Hill, whose house in Belle Harbor, Queens, was badly flooded by Sandy’s storm surge, said she was able to vote outside her district, but only in the presidential and state Senate race.

“I went to a public school here, and I told them I was from the Rockaways and I was displaced, and they let me vote,” she said. “I couldn’t vote for city council and other local races, but that’s all right.”

In Point Pleasant, N.J., where many residents still have no power, Jersey Shore voters encountered long lines at polling places but expressed appreciation for being able to cast their ballots at all.

“It feels extra important today because you have the opportunity to influence the state of things right now, which is a disaster,” said Renee Kearney, 41, of Point Pleasant Beach, the Associated Press reported. An Obama supporter, she said her resolve was strengthened by his response to superstorm Sandy.

“I was extremely impressed by his response to the storm,” she told AP. “For people who were not so certain about him, I think this may have sealed the deal.”

“Oh my God, I have been so anxious about being able to vote,” said Annette DeBona, 73, also of Point Pleasant Beach, according to AP. “It’s such a relief to be able to do it. This is the happiest vote I ever cast in my life.” She said she voted for Republican nominee Mitt Romney because she believes he would “lift us out of our spiritual and mental depression and help us believe again.”

In the Rockaways, a beachfront community in New York’s Queens borough that was devastated by Sandy and a subsequent fire, voting in an unheated tent was delayed for about half and hour Tuesday morning as poll workers struggled with generators, Reuters news agency reported.

Most of the city’s more than 15,000 schools reopened Monday, but 57 sustained structural damage, 19 lacked power and 16 were being used as shelters, officials said.

At one school in the Midland Beach community on Staten Island, poll workers set up flares at an entrance to provide light and moved voting machines outside into tents, where voters lined up in below-freezing early morning temperatures.

New York authorities planned to run shuttle buses every 15 minutes in storm-damaged communities to bring voters to the polls.

Nearly 60 of the city’s 1,350 polling sites were unusable, and voters who normally cast ballots in those places were being directed elsewhere, news agencies reported. In New Jersey, more than 180 polling sites were moved to alternate locations because of Sandy’s effects.

But those changes affected thousands of voters. In New York along, 250,000 residents were being asked to vote at different places, Bloomberg News reported.

In Ocean County along the New Jersey coast, officials used a converted recreational vehicle to bring mail-in ballots to shelters in Toms River, Pemberton and Burlington Township so displaced people could vote.

“This is a Godsend,” said Marc St. James of the 38-foot white Winnebago with the “VOTE HERE” banner taped to it. He has been sleeping on a cot in the gym of the Pinelands Regional High School since his home on Long Beach Island was damaged and officials ordered all residents off the barrier island.

“Several hundred of us were worried about how we were going to vote,” said St. James, 69, who was accompanied by his wife, Joyce. “This is an election of great importance, about which direction the people want to the country to go.”

If the conditions depress turnout, the outcome in New York and New Jersey could become a factor in the national popular vote total, election analysts said. But no impact on the electoral college vote is expected, since both states are considered to be solidly in Obama’s camp.

Lynch reported from New York. Lyndsey Layton in New Jersey contributed to this report.