Former Vice President Joseph R. Biden Jr. leads Mr. Trump among likely voters, 46 percent to 42 percent, while Mr. Tillis is behind Cal Cunningham, his Democratic challenger who is embroiled in a scandal over salacious text messages, 41 percent to 37 percent.

Gov. Roy Cooper, a Democrat, leads his Republican challenger, Lt. Gov. Dan Forest, by a larger margin: 51 percent to 37 percent.

Mr. Cunningham’s lead has held steady since early September, when the Times/Siena poll found the Democrat with a five-point advantage over Mr. Tillis. Fifteen percent of likely voters surveyed said they remained undecided in the Senate race — nearly twice as many as those who said they were undecided in the presidential contest in North Carolina…

The poll was conducted within the last few days, well after Mr. Cunningham offered an awkward public apology for the romantic (but PG-rated) texts he sent this summer to a woman who is not his wife. It found that Mr. Cunningham, a former state senator and an Iraq war veteran, retains a 15-point advantage among women.