BROOKLINE, N.H. >> Jeanne Cleveland, a retired teacher, pursed her lips sourly at the mention of his name and tried to summarize her distaste in diplomatic terms.

“I think he’s arrogant,” she said. “I think he’s rude. I think—”

She paused, reaching for the right words.

“Let’s just say,” she said, “I don’t like the way he represents us as a country.”

To avoid any confusion, Cleveland put it plainly: “I don’t like Trump.”

In this, the retired teacher, 70, from Hollis has ample, baffled and agonized company in New Hampshire as the presidential primary enters its final, frenzied weeks, with Donald Trump remaining atop poll after poll of the state’s Republican electorate.

Or is he? So deep is the dislike for him in some quarters that people like Cleveland’s husband, Doug, question the accuracy of polls that so consistently identify Trump as leading the field with around 32 percent.

“I’ve never met a single one of them,” Doug Cleveland said about those said to be backing Trump. “Where are all these Trump supporters? Everyone we know is supporting somebody else.”

These are the lamentations of the 68 Percent — the significant majority of Republican voters here who are immune to Trump’s charms and entreaties, according to a battery of voter interviews Thursday at campaign events for his rivals.

For months, great quantities of ink, political-science brain power and polling resources have been expended trying to dissect, if not exactly diagnose, the Trump phenomenon — precisely who supports him and why. Far less energy has been devoted to sounding out a much larger segment of the electorate: those who reject him.

From Brookline to Laconia, these voters call Trump “unhinged.” They object to his “temperament.” They doubt his motives.

Their disapproval runs strikingly deep. Several spoke of changing the channel whenever his face (or, more frequently, his New York-accented voice, via telephone) turned up on television.

“I really try not to watch him,” one resident, Paul Brennan, said as he walked out of an appearance by Sen. Marco Rubio of Florida in a factory in Brookline, along New Hampshire’s southern border. “I wouldn’t trust him as far as I could throw him.”

Trust is a nagging, recurring issue among Trump skeptics. On some level, they do not quite believe that he is really, seriously running for president, despite everything, nor are they convinced that his Republicanism is authentic.

They remember his donations to Democratic candidates (since disavowed as a business necessity) and his support for abortion rights (rationalized as trying to fit in with left-leaning New Yorkers).

Charles Bradley, 67, a retired lawyer from Laconia who calls himself conservative, said he had lost count of Trump’s shifting allegiances and discarded positions.

“He loves everybody until he doesn’t love them, if you’ve noticed,” Bradley said. “He loved Ted Cruz, and now he doesn’t anymore. He loved Hillary Clinton, and now he doesn’t anymore.”

But for the 68 Percent, no single attribute rankles as much as Trump’s instinctive proclivity to insult — everyone, over everything, no matter how big or small the issue, from Mexicans to the Fox News journalist Megyn Kelly.

“His behavior — I can’t do it,” Joan Weaving, 72, from Hampton said as she sat on a folding chair next to her husband at a Jeb Bush campaign event Thursday night. “Belittling people. Just seeing the bad parts of things.”

They may share his impatience with ordinary political speak, with the hypersensitivity that has crept into public life. And they admire his attempts to crack and peel away that veneer of politesse.

But they have limits.

Barbara Henry, 63, wants a president with a filter. Any filter.

“He has no filter,” she said, leaning forward to make her point.

“I understand people say, ‘I’m sick of this political correctness.’ I get that,” she said. “But there’s also an argument for some measure of civility. I mean, he’s just not somebody who you can say, ‘I’m proud he’s our president.’”

Several voters insisted they had tried hard to close their eyes and picture Trump as the leader of the free world. They could not do it, they say.

“He’ll lose his cool when he gets up with Putin or one of those, and tell them to go fly a kite,” said Kathy DeFreitas, who lingered at a pizza parlor in Manchester after listening to Sen. Ted Cruz of Texas.

Jim Lowell, 65, a retired Navy commander, served under commanders in chief, so he felt qualified to assess applicants for the job.

“I don’t think he’s presidential,” Lowell said. “I don’t think he has the experience. I don’t think he has the knowledge.”

Some voters interviewed said they wondered what, exactly, a President Trump would do to “make America great again.” Few could pinpoint much of an agenda, besides The Wall, in Trump’s abundant pronouncements.

“I don’t know and I’m not sure he does, to tell you the truth,” said Bradley, the retired lawyer.

Trump’s televised ubiquity has provided voters with an extraordinary amount of raw material from which to judge him — or to make a Trump diagnosis. Several voters offered their unsolicited medical opinions.

“I do believe he suffers from megalomania,” said Lorraine Raleigh, a 68-year-old retired teacher from Hampton.

Ray Weaving, 75, charitably downgraded the condition ever so slightly.

“Egomaniac,” he said.

Trump is fond of describing his followers as a silent majority. But there is nothing quiet about his doubters, whose frustration with him boils over at the campaign events of his rivals.

As Bush campaigned at a veterans’ hall in Manchester a few days ago, Jimmy Kyriakoutsakos, a local voter, dedicated his allotted question not to national security or the plunging stock market but rather to stopping Trump from becoming president.

“I do not know how a carnival entertainer could be running the field, and I’m very disappointed in that,” he told Bush.

Bush wore the pained look of a man who has fielded the question before.

“I try to avoid in these meetings to have a Trump therapy session,” he said.

But then he played therapist anyway, consoling the Trump-averse crowd.

Amid their deep anxieties and doomsday predictions, the 68 Percent do concede that Trump has deftly dominated the Republican race, tapped into the unseen fury of voters and turned once-sleepy debates into must-watch television.

“He’s very entertaining,” Susan Bunting said as she waited to hear Gov. John Kasich of Ohio speak in the lakeside town of Wolfeboro.

A caveat quivered on the horizon.

“But,” she said, “I don’t want an entertainer for president.”