Another poll is showing New Jersey's U.S. Senate race between Democratic incumbent Robert Menendez and Republican challenger Bob Hugin is a tight one -- and that Menendez still needs to win over members of his own party.

Menendez held a five-point lead over Hugin, the former Celgene Corp. executive, among the state's registered voters, and a six-point lead among likely voters in the Fairleigh Dickinson University PublicMind Poll released Wednesday morning.

With margins of error taken into account, the poll called it a "statistical dead heat." And about one-in-five Democrats are undecided.

Menendez led Hugin 43 to 37 percent among likely voters in the poll, and 37 to 32 percent among registered voters. That's similar to his 4-point lead in a May FDU survey among registered voters, the first poll that didn't give Menendez a double-digit advantage and thus forecast a close Senate contest.

Since then, polls by Quinnipiac University (6 percentage points) and Stockton University (2 percentage points) have Menendez ahead, but not by much. Hugin has yet to lead in any legitimate survey.

"There's no denying that this is tighter than one would expect for an incumbent senator," said Krista Jenkins, director of the FDU poll and a political science professor at the university.

Just 73 percent of Democratic likely voters said they would support Menendez, with 22 percent undecided. Hugin, on the other hand, was backed by 89 percent of Republican likely voters, with just 6 percent undecided.

The large number of undecided Democrats followed a two-day gathering in Atlantic City last month, where Democratic National Chairman Tom Perez, Gov. Phil Murphy, Lt. Gov. Sheila Oliver, U.S. Sen. Cory Booker and other officials urged the party faithful to get to the polls and pull the lever for Menendez.

"It's both a blessing and a curse that a good number of Democrats remain up for grabs," Jenkins said. "Partisan leanings are usually a strong indicator of how someone will vote. If Menendez is able to capture the support of undecided Democrats, plus some of the independents, he will be able to decisively pull ahead of Hugin by November. It will be harder for Hugin to do the same, given the smaller base of undecided Republicans in the state."

Menendez also could get a boost from the antipathy that voters have for President Donald Trump. Almost 6 in 10 likely voters, 59 percent, had an unfavorable view of Trump, while less than 4 in 10, 39 percent, viewed him favorably.

Hugin contributed the maximum $5,400 to Trump's campaign and another $233,200 to the Republican National Committee that helped elect him.

Working against Menendez, however, is the fact that more than half of the likely voters polled, 53 percent, viewed him unfavorably, compared with 35 percent who had a favorable opinion of the senator. Hugin was viewed favorably by 36 percent and unfavorably by 30 percent.

Menendez was "severely admonished" by the Senate Ethics Committee for for accepting gifts and trips from a friend and campaign donor, Dr. Salomon Melgen, while intervening with federal agencies on his behalf.

The ethics committee acted after Menendez's trial on corruption charges ended in a mistrial. After the judge acquitted Menendez of some of the charges, the U.S. Justice Department dropped the rest of the case.

Hugin has spent $15.5 million of his own money through June 30 on his campaign, primarily on ads attacking Menendez on ethics.

The poll of 508 likely voters was conducted Sept. 26-30 and had a margin of error of plus-or-minus 4.3 percentage points.

Jonathan D. Salant may be reached at jsalant@njadvancemedia.com. Follow him on Twitter @JDSalant or on Facebook. Find NJ.com Politics on Facebook.