If Mr. Cunningham unseats Mr. Tillis — who has lagged behind Mr. Trump’s support in the state — Democrats would be closer to netting the three seats they need for a Senate majority should Mr. Biden win the presidency.
The party’s prospects of flipping Republican-held seats are considered the strongest in Arizona and Colorado, and they have pickup opportunities in Maine, Iowa and elsewhere. Republicans are well positioned to win a Democratic-held seat in Alabama.
One difference in North Carolina, though, was that the proportion of voters — 15 percent — who were undecided in the Senate race two weeks ago had shrunk to 6 percent. This suggests that voters have come home to their parties, but with no clear advantage for the Republican incumbent in a state closely split along party lines. Independents broke for Mr. Cunningham in the latest poll, 48 percent to 34 percent.
The poll of 1,034 likely voters has a margin of error of about four percentage points.
“I cringe sometimes at the things he says,” Michael Shawl, 48, said of Mr. Trump, whom he voted for both this year and in 2016. “But at the same time, he pushes the policies that he ran on. He’s trying to do exactly what he said he would do.”
Mr. Shawl, who owns a construction and roofing business in Wilmington, N.C., said that the state’s Democratic governor, Roy Cooper, was “killing small businesses” but that the president was not. “I’d like to see him get the economy back on track,” he said of Mr. Trump. “I’d like to see a Covid vaccine released to the world. I’d like to see Obamacare replaced.”
The single race that appeared to have shifted, if only slightly, was for governor. Mr. Cooper held a nine-point lead over Dan Forest, the Republican lieutenant governor. Two weeks ago, Mr. Cooper’s advantage was 14 points. Over the summer, Mr. Cooper refused to yield to Mr. Trump’s demand to loosen coronavirus restrictions to let the Republican National Convention take place in Charlotte.
On Ocracoke Island off the Atlantic coast, Robin Macek, who owns a bed-and-breakfast, voted last week at a fire station for Mr. Biden, a ballot she had been waiting a long time to cast.