“In this environment right now, when people’s actions from 35 years ago are relevant, it makes sense that if you said those words, they should be relevant and go to character,” said Susan Del Percio, a Republican political consultant who has worked with Mr. Faso in the past.

But political observers said that given the makeup of the district, where voters gave both President Barack Obama and President Trump the edge, the negative ads could actually help Mr. Delgado, who lives in Rhinebeck with his wife and two young sons.

“In some ways, it’s a test of how far we have come, whether it matters in that district,” said Christopher B. Mann, an assistant professor of political science at Skidmore College. “It’s hard to say whether it will be a pivotal factor or maybe to his advantage. The ads have drawn national attention, and they’ve raised Delgado’s profile.”

Since the first radio ad started airing in July, Delgado campaign officials said they have seen a shot of energy. In August, some 500 volunteers knocked on 13,000 doors and made 32,000 phone calls.

On the campaign trail, Mr. Delgado criticizes Mr. Faso’s votes to repeal the Affordable Care Act and to increase work requirements for people receiving federal food assistance. According to FiveThirtyEight, the data journalism website, Mr. Faso has a “Trump score” of 89 percent in a measure of how often he has voted to support the president’s position.

Having spent recent months in Washington, Mr. Faso is playing catch-up on his campaign. In the 24 hours after arriving in the district last Friday, he attended two high school football games, a veterans event, a business fair, an Elks Club barbecue, a Knights of Columbus dinner and a sportsmen’s club meeting, among other events.

Mr. Faso is nervous that scorn for Mr. Trump among Democrats could cost him a seat he has held for just one term; the district has more registered Democrats than Republicans. Mr. Faso, too, is bitter about what he calls misleading attack ads against him, particularly about his voting record on health care.