Voting in the state was complicated by Hurricane Sandy, with many polling places still without power or even underwater on the Jersey Shore, and many residents still unable to return home. Lt. Gov. Kim Guadagno announced Tuesday afternoon voters who had applied to cast ballots by email or fax would be able to do so through Friday.
With 2810 of 6,338 precincts reporting, Obama led Republican nominee Mitt Romney 59 percent to 40 percent, WHYY-FM in Philadelphia reported.
The state has become more Democratic in recent presidential elections. President George H.W. Bush won the state in 1988 continuing a string of Republican victories in New Jersey but lost the state four years later.
Menendez, who was appointed by Gov. Jon Corzine in 2005 to fill his own unexpired term, had 61 percent of the vote to 37 percent for his Republican challenger, state Sen. Joe Kyrillos. Menendez, born in New York to recent immigrants from Cuba in 1953, was the first Hispanic elected to the Senate from a northeastern state.
New Jersey has not been represented in the Senate by a Democrat for several decades.
Late Tuesday, a judge refused to order New Jersey to let voters affected by Hurricane Sandy use the federal electronic ballot for overseas voters.
The American Civil Liberties Union made the request on behalf of three Essex County women who are living outside the state temporarily because of Sandy, The Star-Ledger of Newark reported. The ACLU said all three had trouble accessing the state's emergency system to request electronic absentee ballots.
The state government and the campaigns of U.S. Sen. Robert Menendez and his Republican challenger, State Sen. Joe Kyrillos, opposed the ACLU.
Superior Court Judge Walter Koprowski said he did not believe he had the authority to order the state to change its procedure. Lt. Gov. Kim Guadagno said Tuesday afternoon electronic ballots submitted by Friday will be counted.
"If the email was bumped or sent back, it has to be the duty of the clerks to address those issues to make sure those applications are processed," Koprowski said.
Voters had until 5 p.m. Tuesday to apply for ballots and then must submit the chits by 8 p.m. Friday, The Star-Ledger said.
Gov. Chris Christie said Tuesday's voting was going smoothly, albeit plagued by long lines and confusion about polling places in the state's hardest hit counties.
Christie, in an appearance at Berkeley Elementary School in Westwood, said only 100 of the state's 3,000 polling places were impacted by the storm, which hit a week ago, causing deaths, wrecking the shoreline, destroying homes and displacing thousands. More than a half-million homes and businesses still were without power.
"Only people who should be applying for their ballots online are voters affected by the storm," Christie said. "Everyone else, get your butt up and go to your polling place like normal."
The state set up a text system for voters to find out where to vote. Voters were instructed to text "WHERE" to 877877, but the system was plagued by errors early in the day. Updated databases were uploaded after the errors were discovered and the system was fixed, state officials said.
"I don't have complete confidence in the text # due to feedback," Newark Mayor Cory Booker tweeted. He advised his residents to check the city's website or call (973) 733-4311.