About a third of North Carolina Republicans (32 percent) said it’s time to give a new person a chance, compared with 39 percent who said Tillis has done a good-enough job to deserve re-election. That metric also places him second-to-last among Republicans seeking re-election.

“There seems to be more chatter about Tillis facing a primary than anyone else,” said nonpartisan political analyst Nathan Gonzales in an email Wednesday. “But his critics need a candidate. You can’t beat someone with no one.”

No candidate has emerged to challenge Tillis from his right, so far, despite the apparent opening. One potential candidate, Rep. Mark Walker (R-N.C.), has not ruled out a possible bid, though Republican sources in the Tar Heel State think he’s leaning against it. A spokesman for Walker said in an email Wednesday that he is “not currently planning to primary Thom Tillis” and “will continue to use his platform to support President Trump’s agenda.”

One conservative operative in the state said Tillis has a trust problem, with moderates questioning his independence from the president and conservatives questioning his loyalty.

Asked about his case to the Republican electorate, Jordan Shaw, who heads the Republican firm OnMessage Inc.’s Charlotte office and is advising Tillis’ re-election campaign, said the senator has stood by Trump many times despite his hesitance on the issue of the emergency declaration.

“You’re going to be hard-pressed to find a lot of results-oriented differences between Tillis and the president,” he said.

Tillis is not the only senator with a low net approval at home.

Sen. Cory Gardner (R-Colo.) is the least popular Republican with his home base, with 49 percent approving and 28 percent disapproving. But the man viewed widely as the most vulnerable incumbent seeking re-election next year has faced no talk of a serious primary challenger, as several Democrats are lining up for their party’s nod to compete for the seat.