Sen. Robert Menendez’s popularity in the Garden State has taken a big hit following the drumbeat of media reports about his alleged improprieties.

In a new poll from Quinnipiac University, 41 percent of registered New Jersey voters surveyed said they disapprove of the way Menendez is handling his job as senator, while only 36 percent approve. A month ago in a similar poll, 51 percent approved and 33 percent disapproved.

Twenty-eight percent of those polled said Menendez was “honest and trustworthy,” while 44 percent said he was not.

Those numbers would be daunting for any incumbent facing re-election. But Menendez, the chairman of the Foreign Relations Committee, will not face voters until 2018. He won re-election with 59 percent of the vote last November.

Another Democrat, Newark Mayor Cory Booker, on the other hand, is exploring a run for the state’s open Senate seat in 2014. He fared well in the poll, with 59 percent saying they had a favorable opinion of him and only 11 percent seeing him unfavorably. Potential Republican candidate Geraldo Rivera didn’t do as well: only 20 percent had a favorable opinion of him, with 39 percent seeing him unfavorably.

The Quinnipiac University poll used live interviewers to survey 1,149 registered voters on land lines and cellphones Feb. 13-17. The poll’s margin of error was 2.9 points.