“Obviously many of my supporters have donated to the Democratic Senatorial Campaign Committee. So, at the end of the day, if they think we need it, maybe they’ll spend it,” Mr. Menendez said in North Bergen on Sunday. “We’ll see.”

On paper, Mr. Menendez has several factors in his favor: New Jersey is one of the bluest states in the country, with 920,000 more registered Democrats than Republicans.

As a result, national Democratic groups have been reluctant to pour resources into New Jersey since they have so many competitive races elsewhere, from protecting Senators Bill Nelson in Florida and Joe Manchin in West Virginia to boosting the promising campaigns of Beto O’Rourke in Texas and Phil Bredesen in Tennessee.

But perhaps in a small sign that national leaders were heeding the worries of local Democrats, the Senate’s campaign committee recently set aside $400,000 for coordinated advertising in the race, still a modest sum given that New Jersey sits between New York and Philadelphia, two of the country’s largest and most expensive television markets.

The campaign committee defended its focus on races elsewhere, believing that Mr. Menendez will prevail next month. “Bob Menendez’s record fighting for New Jersey is second to none,” said David Bergstein, a spokesman for the group. “We are confident that the people of New Jersey will have his back this November just as he has had theirs throughout his entire career in public service.”

So far, Mr. Menendez has been drastically outspent on television. Mr. Hugin, a wealthy former pharmaceutical executive, and a super PAC supporting him, Integrity NJ, have spent a total of $3.8 million on television advertisements in the past month, according to Advertising Analytics. In the same period, Mr. Menendez spent $20,000.