Sen. Robert Menendez (D-N.J.) speaks at a news conference on March 26 in Newark. (Kena Betancur/Getty Images)

This post has been updated.

The New York Times, New Jersey's Star-Ledger and scads of columnists agree: Sen. Robert Menendez (D-N.J.) should step down from his seat in light of a pending 14-count federal corruption indictment.

Here's who doesn't agree: Most of Menendez's constituents.

A Rutgers-Eagleton Poll released Tuesday showed that 58 percent of New Jersey residents believe that Menendez, who has represented the state in Congress for 22 years, should be allowed to stay in office unless he is found guilty.

[Sen. Robert Menendez indicted on corruption charges]

Prosecutors say that Menendez used his office to benefit a political supporter, Florida eye doctor Salomon Melgen, in return for lavish gifts, trips to Melgen's Caribbean home and hundreds of thousands of dollars in campaign donations. Menendez pleaded not guilty Friday and vowed to fight the charges.

The poll, which reached 860 New Jersey residents in the days leading up to and following the indictment, found that Menendez can rely on a significant base of support, with about one-third of residents having a favorable impression of him -- about the same as in nearly a decade of prior Rutgers polling.

About three-quarters of poll respondents had heard at least a little about the Menendez allegations, both before and after charges were filed Thursday. However, the roughly one-third of poll respondents who were reached after the indictment had a more unfavorable impression of him than those reached beforehand. And those who say they have heard a lot about the allegations are significantly more negative toward Menendez.

The drop seen after the indictment "may eventually lead to more people preferring that Menendez step down rather than fight," Rutgers-Eagleton polling director David Redlawsk said. "For now, though, many may be giving him the benefit of the doubt.”

Said Tricia Enright, Menendez's spokeswoman, "The people who know Bob Menendez best believe they are best served having him on the job, fighting for them, as he has done his entire career. And he has no intention of letting them down."

While those who say they regard Menendez favorably are more likely to want him to stay in office while he fights the charges, more than 40 percent of those who don't like him or who disapprove of the job he's doing as senator also think he should stay. The poll showed little difference in opinion on that point between Democrats (63 percent of whom said he should stay) and Republicans (61 percent).

Another thing New Jerseyans tend to agree on: Political corruption isn't a particularly New Jersey problem.

According to the poll, 6 in 10 residents of the state say that New Jersey is about the same or less corrupt than other states. And only 15 percent of poll respondents said government corruption is the most important problem facing the state; more cited taxes and the economy as their top issue of concern.