Democrats are pleading with Senator Menendez of New Jersey to resign and spare them a messy expulsion, after a federal jury convicted him on all counts in his corruption trial. The outcome could be a boost for the GOP senatorial candidate, Curtis Bashaw, and for President Trump, both of whom have been chipping away at the state’s blue wall.

The national parties have long written off New Jersey voters as resigned to corruption. Mr. Menendez’s crimes, though, are the kind that can sway an apathetic electorate. Both Trump and Mr. Bashaw, the latter of whom has called on Menendez to resign, are helped by the corruption trial’s fallout.

Democrats hold all statewide offices in the Garden State. It hasn’t elected a Republican to the presidency since 1988 or to the Senate since 1972, a drought second only to Hawaii’s. Their party has no fingerprints on the long tolerance of Menendez, who has been plagued by scandals before.

“Beyond profiting off of his United States Senate seat in accepting bribes in the form of gold bars and cash,” Jeanette Hoffman, spokeswoman for Mr. Bashaw, tells me, “Senator Menendez was convicted of acting on behalf of a foreign government, and therefore poses a national security risk.”

The GOP benefits from having, in Mr. Bashaw, an outsider, a “married, gay man,” as he described himself to me. An entrepreneur who restored Cape May’s historic Congress Hall, he defies opponents to “put me in a box” after beating a Trump-backed candidate to win the primary.

Majority Leader Schumer, in the Senate, as well as Congressman Andrew Kim, and others on their side, are pushing for Menendez to end the drama. With troubling poll results, time is short to put his scandal in the rearview mirror.

A survey of registered voters, conducted by a Republican PAC called United 2024, was released before Menendez’s conviction. It found that both the Senate and presidential races in New Jersey were within the margin of error — whether or not independent candidates were on the ballot.

A strategist for United 2024, Matt Mowers, said that his poll shows “voters have soured on the Biden-Harris administration and are ready to punish Democrats running down ballot” — like Mr. Kim.

In the poll, Trump edged President Biden 43 percent to 41 percent in a two-way race and they’re tied at 38 percent when other candidates are included — one reason Democrats have sued to keep the independent, Robert F. Kennedy Jr., off New Jersey’s ballot.

Mr. Kim led Mr. Bashaw 41 percent to 39 percent. With the margin of error at 4.5 percent, it’s a statistical tie that held even when Menendez, running as an independent, was an option. A survey of likely voters, conducted in late June by the independent group co/Efficient, found similar results.

Mr. Biden trailed Trump 40 percent to 41 percent, with a 3.42-point margin of error. Seven percent favored other candidates. In a three-way race, Mr. Kim led Mr. Bashaw 39 to 33 percent and 41 to 34 percent in a two-way race.

If Menendez heeds the call to pull out of the race, Governor Murphy would name his replacement. Ms. Hoffman said that the Democrat appointing Mr. Kim “would be a continuation of the inside deals and machine politics that habitually dominate New Jersey politics.”

Removing Menendez from the Senate would be a headache for Democrats. It would require two-thirds of the upper chamber, a high bar of 67 votes. The Senate has expelled just 15 members in its history, and 14 of them were Democrats — for backing the Confederacy during the Civil War.

The first senator to be expelled was William Blount, a Tennessee Democratic-Republican, in 1797, for what the Senate describes as concocting “a scheme for Indians and frontiersmen to attack Spanish Florida and Louisiana, in order to transfer those territories to Great Britain.”

Senator Long of Louisiana was investigated for possible expulsion over allegations of corruption, but the Senate in 1934 determined that “the charges and evidence were insufficient to warrant further consideration.”

Given that New Jersey’s electoral votes and Senate seat would be just as significant to Washington’s balance of power as any others, Republicans and Democrats are starting looking to the motto of the state lottery — “anything can happen in Jersey.”

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Corrections: The Senate investigated Senator Long of Louisiana for possible expulsion but in 1934 deemed there was insufficient evidence to do so. An earlier version misstated the outcome of the Senate investigation of Long.

Fourteen is the number of Democratic members of the Senate to be expelled. An earlier version misstated the number of of expelled Democratic senators.