Republican presidential candidate Donald Trump waves as he leaves the stage Dec. 10 after speaking at a meeting of the New England Police Benevolent Association in Portsmouth, N.H. (Mary Schwalm/Reuters)

Mary Donnelly agrees “150 percent” with Donald Trump’s “very positive” idea to temporarily bar most Muslims from entering the United States.

“You can’t tell people: ‘If you’re not going to convert to my religion, I’m going to cut your head off.’ You can’t do that. . . . That does not belong in this country,” said Donnelly, 58, a campaign volunteer who stood with other supporters outside Trump’s latest campaign event on Thursday evening. “We’re a country that loves one another, no matter what the race.”

Nearly every prominent Republican has denounced, or at least disavowed, Trump’s call on Monday for a ban on Muslims in the wake of Islamic State-linked terrorist attacks. But most of party’s voters appear to agree with the front-runner, once again putting the Republican base at odds with its establishment and posing another vexing challenge for GOP leaders who fear that Trump’s dominance of the race for nearly six months is doing irrevocable damage to the party’s brand.

Fifty-four percent of Republicans surveyed by CBS News on Wednesday and Thursday agreed that Muslims should be temporarily banned from entering the country, even though one-third of those conceded it would go against the nation’s founding principles. With the public overall, the proposed ban was far less popular, with 58 percent saying they are opposed.

“The more outrageous he is, the more support he gets — in a way, he’s brilliant,” said Jim Luther, a former GOP state senator backing Sen. Marco Rubio (R-Fla.).

Republican presidential candidate Donald Trump smiles as he has his photograph taken with supporters after being endorsed at a regional police union meeting in Portsmouth, N.H., on Dec. 10. (Charles Krupa/AP)

While Trump appeals to conservatives, he is likely repelling women and minorities, who are key to winning swing states and competitive general elections, said Fergus Cullen, a former New Hampshire Republican Party chairman who remains undecided in the race.

“I’ve done the math. If we get 120 percent of the angry white male vote, we still can’t win,” Cullen said. “The Beatles didn’t invent teenagers, but they played to that audience. Donald Trump didn’t create nativism within America — it’s always been there — but he’s bringing it to the surface in a very ugly way.”

The panicked concerns from party elders delight many of Trump’s fans, who say they are tired of career politicians and feel let down by the party. Outside a private meeting Thursday night between Trump and a regional police union that had endorsed him, there was strong support for the ban among about two-dozen Trump supporters gathered with campaign signs. There was also broad agreement that the media has misreported the candidate’s proposal and that Republican leaders such as House Speaker Paul D. Ryan (R-Wis.) were wrong to condemn it.

Donnelly said she likes Trump because “he’s trustworthy, he’s honest and he’s humble; plus, nobody owns him.” Even if the Republican National Committee finds a way to overrule voters and pick a nominee other than Trump — something his fans are increasingly worried about — Donnelly said she would vote for him as an independent, if he were to decide to run as one.

“I’m right there, and I think all the other Republicans that are voting for Mr. Trump are going to do the same,” said Donnelly, a state employee who lives in Concord and recently changed her registration from independent to Republican.

Down the block and across the street were about 200 liberal activists with homemade signs collectively labeling Trump as a fearmongering bigot using Muslims as a scapegoat. One sign declared Trump to be “America’s Hitler,” and several protesters taped gold Stars of David on their winter coats as Jews in Germany once did.

The Trump camp tried to drown out the protesters’ singing and live band by blaring Twisted Sister’s “We’re Not Gonna Take It.”

A police officer stands across the street from protesters outside a campaign stop for presidential candidate Donald Trump at a meeting of the New England Police Benevolent Association in Portsmouth, N.H., on Dec. 10. (Mary Schwalm/Reuters)

Richard Travers, a 74-year-old Trump volunteer from Massachusetts, said the businessman’s call for a short-term ban is no different than President Jimmy Carter barring people from Iran during the hostage crisis in 1979.

He said career politicians have become too indebted to their donors and special interest groups, and the media no longer reports the truth.

“They’ve all lost their credibility, so the only one that’s got credibility — as far as the vote of America is concerned right now — is Donald,” he said.

Travers says Trump began by calling for an all-out ban as a negotiating strategy, not because that’s what he wanted. “When you want something, you start a lot higher, then you negotiate down until they say, ‘Oh, that sounds reasonable,’ ” he said.

But should world leaders really treat the movement of human beings in and out of a country like details of a real estate contract?

“You do when you’re in a war,” responded Travers, who was wearing a camouflage ball cap with Trump’s slogan on it. “We’re in a war with Islamic extremists.”

Inside the hotel, Trump briefly spoke as he accepted the endorsement of the union.

“We’ve had a pretty interesting couple of days — we have people talking, I will tell you that,” Trump said to gentle laughter. “And we have them talking very positively because people are saying: ‘You know, Trump is right.’ ”

That same night, about 60 miles southwest at a sports club in Milford, N.H., a small audience waited to hear from former Florida governor Jeb Bush, who has called Trump “unhinged” for proposing the ban.

Marcia Foster, a real estate broker from Mason, said Trump has a point with his proposed ban, although he “could have worded it differently.”

“The only ones who want to kill us are Islamic terrorists, so it makes sense that you vet them,” said Foster, a registered independent. “There aren’t too many Christian churches that teach Christian terrorism.”

But one of Foster’s neighbors sitting next to her had a different reaction.

“My God, we can’t block everyone from coming in who’s Muslim,” said Kerry Hamel, a political independent and occupational therapist whose son is dating a Muslim woman.

“It’s Trump being Trump,” said her husband, Scott Hamel, a registered Republican who works for a supply chain engineering company. He’s torn on the issue: “I don’t think we’ve done enough to vet people, but the practicality of shutting it all down — I just don’t think it’s practical.”

Foster interjected: “It would just be temporary.”

“Yeah, but it could take two years,” Hamel said. “I thought it would not be practical.”

Back in Portsmouth, activists slowly encroached on the corner occupied by the Trump supporters, a few carrying signs for presidential candidate Sen. Bernie Sanders of Vermont. They sang along to Twisted Sister but changed the words: “We’re not going to take Trump anymore!”

A Trump supporter added a refrain of his own that didn’t exactly fit: “Sanders is a socialist!”

There were some conversations between the two camps, but no conversions. Donnelly said she doesn’t care what the protesters say, what their signs say, what the establishment says, what the party says. She believes in Trump.

“The silent majority needs to be heard,” she said. “We have been in a mess in this country, and it’s got to stop. We have to fix it.”

O’Keefe reported from Milford, N.H. Scott Clement also contributed to this report.