Within South Jersey, which leans heavily Democratic, Menendez's edge is even more pronounced: 48 percent to 28 percent among those who have made up their minds or are leaning toward one candidate - notwithstanding the fact that the senator lives in Hudson County, in the northern end of the state.
Still, a quarter of voters statewide have not yet decided, and many have not formed solid opinions of either rival.
"This is a movie where the voters are still watching and haven't walked out yet," said Plaut, whose firm is Democratic. The Republican firm that took part in the poll is National Research Inc.
Statewide, the poll of 600 likely voters has a margin of error of plus or minus 4 percentage points; the pollsters said; they put the margin of error for the smaller sample of 134 likely voters in seven South Jersey counties at 8.5 percentage points.
Only 60 percent of likely voters knew enough about Menendez to offer a view of him, despite his having served nearly a full Senate term after a long House career. Among those who did know of him, 33 percent saw him favorably compared with 27 percent with an unfavorable view.
Kyrillos, though, faces an even steeper climb when it comes to introducing himself: 59 percent said they hadn't heard of him. (Only 22 percent said they had not heard of Menendez.)
Just 23 percent of New Jerseyans have formed a view of Kyrillos, a state senator from Monmouth County, with 15 percent viewing him favorably and 8 percent unfavorably, the poll found.
The low profiles of each candidate reflect the challenge of running statewide in New Jersey, Plaut said: The state is split between two massive media markets, Philadelphia and New York, making it hard for a candidate to get attention and expensive to advertise.
Even Frank Lautenberg, a New Jersey Democrat who has held his U.S. Senate seat for nearly three decades, is familiar to just 63 percent of his home state's voters.
"Sen. Menendez appreciates the support of the people of New Jersey. He shares a strong bond with them because he shares their values and addresses their concerns," Menendez campaign manager Michael Soliman said in a statement. "Sen. Menendez knows that New Jersey's middle class is under attack, and that's why he is fighting back to save and create thousands of jobs, to increase access to health care, to keep the doors open to education and to protect Medicare and Social Security."
Kyrillos' camp seized on the poll's finding that only 60 percent of voters knew enough about Menendez to offer an opinion. A news release from Kyrillos campaign manager Chapin Fay said: "When our [advertising] peaks, rest assured that New Jerseyans will be well acquainted with his failed record in the Senate and Sen. Kyrillos' record of reform."
Follow-up interviews confirmed the limited impressions the candidates have made on voters. Several poll respondents reached by phone said they didn't know enough about the race to comment.
One said all he needed to know about Kyrillos was his party. "I'm voting to just get Republicans in there," Michael Wall of Marlton said. "I'm sick of Democrats in general. They're killing the middle class in New Jersey."
Roy Levinson, a Democrat from Cherry Hill, said there should be a good reason to unseat an incumbent, and he sees no such reason this time.
"Bob Menendez has done a terrific job, and I support what Bob Menendez stands for," Levinson said, citing his stands on social issues and his support of Israel. "I think he's strong for New Jersey, I think he's strong for our nation."
While both candidates have tried to win over women voters, Menendez leads in that group by better than a 3-2 ratio. He also is way ahead among minority voters - 62 percent to just 4 percent for Kyrillos.
The GOP challenger does best among white voters, where he leads by 41 percent to 36 percent.
Contact Jonathan Tamari at email@example.com or follow on Twitter @JonathanTamari.