All eyes are on Senator Menendez in New Jersey’s Senate race after Governor Murphy’s wife, Tammy Murphy, announced that she would drop out of the race just before the deadline to file for the June 4 primary.

Monday is the deadline for Senate candidates in New Jersey to file to run as Democrats ahead of the state’s June 4 primary. Sunday, Ms. Murphy dropped out of the race, saying “I will not in good conscience waste resources tearing down a fellow Democrat.”

“It is clear to me that continuing in this race will involve waging a very divisive and negative campaign, which I am not willing to do,” Ms. Murphy said in a video statement.

The last wild card in the Senate race is the incumbent, Mr. Menendez, who has teased that he may file to run as an independent if he can clear his name before the June 4 deadline.

The later deadline will give the embattled senator a couple of extra months to chart his course ahead of what would no doubt be an uphill battle to win re-election in the Garden State.

Last year, Mr. Menendez was charged with using his position as chairman of the Foreign Relations Committee to act on behalf of Egypt as well as accepting bribes — including gold bars and a Mercedes — in exchange for political favors.

This month, Mr. Menendez and his wife, Nadine Menendez, were charged in a new federal indictment with obstruction of justice, with prosecutors accusing them of lying to their lawyers, who in turn provided inaccurate information to the court.

Mr. Menendez’s case is set to go to trial on May 6, meaning the case will likely be resolved ahead of the deadline for Mr. Menedez to run as an independent. Mr. Menedez teased this possibility in a video last week.

“I am hopeful that my exoneration will take place this summer and allow me to pursue my candidacy as an independent Democrat in the general election,” Mr. Menendez said.

In the video, Mr. Menendez reiterated that he maintains his innocence, saying that “the present accusations I am facing, of which I am innocent and will prove so, will not allow me to have that type of dialogue and debate with political opponents that have already made it the cornerstone of their campaign.”

While Mr. Menendez successfully won re-election after his first brush with the law in 2015,  it’s clear that this time, most New Jersey voters are ready to move on.

A Monmouth survey from early March found that Mr. Menedez’s approval rating among registered voters stands at just 16 percent, and only 5 percent of respondents reported believing that he is not guilty.

In a general election, Mr. Menendez would face a rising Democratic star in New Jersey politics, Congressman Andy Kim, who announced his candidacy almost immediately after the first indictment against Mr. Menendez was unsealed last fall.

In sharp contrast to Mr. Menendez, Mr. Kim has positioned himself as a reformer and is suing to end the county line system in New Jersey, a system that gives the endorsees of county-level party bosses a more favorable spot on the ballot.

While Mr. Menendez could risk playing the spoiler as an independent general election candidate, Mr. Kim could still win the state. In 2018, Mr. Menendez won his last re-election by 11 points more than the Republican candidate, Bob Hugin.