“I believe when we make that contrast and we talk about our successes, that we’re going to have a great victory,” he said. “So that’s how we’re going to change the dynamics of the race.”

Mr. Menendez also cited his legislative record — from fighting for victims of Hurricane Sandy to protecting federal programs for autism — and said that the more time he spends on the campaign trail, the more of a chance he has to remind voters of his achievements in Washington instead of his 11-week trial in Newark. His campaign messaging has so far focused on protecting New Jersey from Trump administration policies, particularly on environmental issues, education, immigration and health care.

“What I believe is that the seeds that I have sown over nearly a lifetime, but certainly in the last six years, all of these things that I have mentioned and many more, we don’t just do it at election time, we do it all the time,” said Mr. Menendez, who has been in the political arena since running for a local school board at age 20, was elected to Congress in 1992 and appointed to the Senate in 2005.

Democratic Party leaders assumed Republicans would target Mr. Menendez given the ethical cloud that has lingered over him, but they believe Mr. Menendez will prevail despite Mr. Hugin’s aggressive and highly visible campaign.

“Bob Menendez will have the full weight of the state party and outside apparatus living and breathing his race every day,” said Elizabeth Gilbert, the executive director of the New Jersey Democratic State Committee. “And Democrats are not coming out and voting for Bob Hugin. It is no secret the results of the Democratic primary were a surprise, but there is a major difference between that and the November election. Democrats are solidly behind Senator Menendez, as are many independents.”

There has been no recent polling on the race, so it is hard to tell whether Mr. Hugin is gaining any traction among voters. In addition to targeting Mr. Menendez, Mr. Hugin’s campaign has focused on addressing the many factors contributing to the high cost of living in New Jersey.