“It’s going to be hard to defeat an incumbent based on normal red and blue teams,” he said.

That may be good news for vulnerable Republican senators and Democrats in the House, who have shifted from traditional campaigning to Zooming town halls with health experts and intense constituent service around small-business loans and unemployment benefits.

All told, as many as nine incumbent governors will be on the ballot in November. The Cook Political Report, a nonpartisan handicapper, rates three of the Republicans and two Democrats as “solid” for re-election. Three Republicans, including Mr. Sununu, are “likely” to retain seats. There is one open governorship, in Montana, which Cook rates a tossup (while Utah’s open seat is a virtual lock to stay in Republican hands).

Mr. Cooper’s race in North Carolina is rated “lean Democrat,” the most competitive of all the incumbents’ contests.

His Republican opponent, Mr. Forest, is a social conservative who strongly backed a 2016 law that required people to use public bathrooms corresponding to the gender on their birth certificates. After it became a target of national ridicule and boycotts, Mr. Cooper made its repeal a top campaign issue. He narrowly defeated Gov. Pat McCrory, the only Republican governor to lose in 2016. The bathroom law, known as H.B. 2, was tossed out.

Many North Carolina voters split their tickets in 2016, voting for both Mr. Trump and Mr. Cooper because of opposition to the bathroom law or a desire to put a check on the Republican legislature. It is unknown how many of those Trump voters will stick with Mr. Cooper this year.

One of them, David Lindsay, a mortgage loan officer for a bank in Cabarrus County outside Charlotte, said he would “reluctantly, most likely” vote for Mr. Trump again. “I’m aware he’s an idiot and sticks his foot in his mouth, that’s no shock,” he said. “But I think a lot of the time he does have the United States’ best interest in mind.” He said Joseph R. Biden Jr., the presumed Democratic nominee, “seems to be stumbling and not knowing what he’s talking about a lot of the time.”

Mr. Lindsay, 37, was undecided about the governor’s race. “I do think Governor Cooper has done a pretty good job since he’s been in office,” he said, including his handling of the coronavirus. “I almost wish it would have been a little stricter. If this thing is as bad as everybody reporting it thinks, we have to nip it in the bud.”