Donald Trump came out swinging in Sunday’s debate with Hillary Clinton, after a calamitous few weeks that saw him falling steeply in the polls and spurned by growing numbers of Republican officeholders. They’ve been recoiling from his disasterous first debate in September, followed by weeks of negative headlines about taxes, and tweets, and most explosively, a lewd video from 2005.

But none of it seems to rattle his core supporters, including those interviewed at random outside supermarkets and chain stores strung along William Floyd Parkway in Shirley recently.

Trump’s supporters in this working- to middle-class hamlet on the south shore of Brookhaven Town are cheerfully steadfast in their choice for president of the United States. The tempest that may sway undecideds or push Clinton-leaning voters to her is seemingly not ruffling Trump’s underlying base, which remains firmly anchored in his oft-stated positions and his demeanor.

“Anybody I speak to is for Trump,” said Judi Trangucci, 71, of Shirley, a receptionist and vice president of a family construction firm, who says she follows the news and debates closely. “Trump has a good heart and loves this country.”

The controversy over Trump declaring a $916 million loss in 1995 that could have let him avoid paying any federal income taxes for at least 18 years? “It’s all legal,” she said. The video where he told then-“Access Hollywood” host Billy Bush how he could do anything to women — and described exactly what — because he was a star? “He’s a man. Men are dogs. All of them,” she said. “Who cares? Look what Clinton’s husband did.”

In fact, even Trump’s widely criticized first debate served to bring Brian Delee, 30, a pressman from Shirley who had been wavering in his support back into his corner. “I like the way he carries himself, I like his sternness with everything,” said Delee. “He’s not one to sit back and wait for things to get done.”

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After sinking to a virtual tie in September, Hillary Clinton’s numbers in the most recent national polls have risen sharply: some polls have her in a double digit lead in a four way race with Trump and third party candidates Libertarian Gary Johnson and the Green Party’s Jill Stein. Pundits are questioning whether Trump can rebound, as they wait for polls reflecting his second debate performance (and more possible revelations on the Clinton camp’s hacked emails.) But his pacing, aggressive attacks were credited with shifting the narrative of a candidate in meltdown, and gratified supporters who were especially pleased by his jibes about investigating and jailing Clinton should he win.

Not everyone in these hamlets are Trump fans, of course. Not the voters who react with distaste when they say his name, or the voter who wouldn’t give her name because she was raised in a country with a dictator and says when she sees one, she knows one: “You can say that I’m afraid.”

Not Helena Cote, a retired security guard who says, “Forget that Trump, he’s a horrible man, he’d bring us back to the Stone Age in World War III,” or Ray Keenan, 64, an attorney and civic group leader, who sees Clinton’s issues as less serious than Trump’s.

“The man is totally unqualified to hold any public office let alone the presidency,” he said. “It’s somewhat surprising to me that Trump has as much support as he has locally.”

School bus drivers, construction workers, truck drivers, store clerks, retirees, people on disability, men and women, old and young, they’re voting for the billionaire, they say. They like his stances on immigration and refugees, on renegotiated trade agreements, on gun rights, on the Wall, and there doesn’t seem to be much Trump could say or do that would dissuade them.

“I’m voting for Trump because he can’t be bought,” said Rob Lattanzio, 34, pausing by his truck outside a supermarket on his way home from work as a commercial playground installer. “There’s nobody out there with a clean slate, nobody’s perfect.”

The influx of immigrants, documented or otherwise, to suburbs such as those in Suffolk, is disturbing to many Trump voters, who see newcomers filling the school buses they drive, or undocumented immigrants undercutting higher-paid union workers. That’s what motivates Joe Kasprzyk, 38, who works at Suffolk Cement, Teamsters Local 1205, to support the Republican candidate, as well as a 47-year-old union electrician from Shirley who would only give his first name, Tony, because his union endorsed Clinton. “A lot of union members are voting Trump because non-union companies are using illegal immigrants and unskilled labor,” he said. “He’s the lesser of two evils.”

Kathleen Marchelewski, 60, of Mastic Beach, is a school bus driver and “basically a Republican” with a long dislike of the Clintons. Building a wall and deporting people would be “great,” even if not necessarily possible, she said.

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“I understand to a certain extent why they’d come in illegally, I’m not a hater,” she said, “but when it comes down to it, it ends up costing me in my paycheck.” Clinton’s election, she said, would frighten her because she thinks she might “open the borders” and let in ISIS terrorists among the refugees.

The criticism of Trump from establishment Republicans and Democrats only makes William P. Benson, 72, a retired New York City police officer, want to vote for Trump the more. “In my life, I’m doing fine,” he said, “but I see people suffering all over. I trust him that he’s going to try . . . We want drastic changes in Washington D.C. and since the Republicans don’t want him, and the Democrats don’t want him, we want him.”

Benson, a long time Shirley resident living now in Brookhaven, said he would continue to support Trump despite his lewd video, which Benson said didn’t reveal anything unexpected about Trump’s character, or his poor first debate performance.

“I thought he was a complete idiot, but he’s the only idiot we have who will make a change in Washington,” he said. “Sometimes you need a disgusting person to make a change.”

But Trump’s temperament and sometimes rash statements have turned off and frightened voters such as Jennifer Bryant, 53, a hospital billing supervisor who wanted experience in the White House, “not a hot head,” and Maria Soto, 55, of Mastic, who called Trump “cuckoo in the head” and a threat to the future.

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And there’s financial analyst Madeline McGowan, 47, who simply likes Hillary Clinton. “I think she’ll be a fair president. She cares. I think she has compassion for the people.”

A sense of anxiety floats around any discussion of the election, as voters look at their own circumstances and worry about whether leaders hear their concerns and can do anything about them. There’s the familiar angst of dissatisfied voters stuck in tense indecision, wondering where to put their faith in a rough election season when both choices are unappealing to them.

“Taxes, extramarital affairs . . . What are you really going to try to do for us?” complained Kim Myers, 58, an administrative assistant from Shirley who is undecided.

The raw personal attacks left many voters troubled and embarrassed by the spectacle, including Clinton supporter Lorraine Pyne, 56, of Shirley, a barrista who originally supported Vermont Sen. Bernie Sanders, and who said of the town hall debate: “There are no words. I was very embarassed as an American and as a woman that Trump would even be considered.” And it put off Suzanne Van Epps, 60, a secretary from Mastic who was leaning toward Trump out of party loyalty from voting at all. “I watched five minutes of the second debate giving them a chance, then I was done,” she said. “I’m embarrassed as a Republican.”

But none of this matters to Trump supporters such as Jay Fried, 43, a truckdriver from Mastic Beach, who said he and all his family were “all for Trump.” He said his daughter is in the U.S. Marines and he has many family members who are in or were in the military. “I don’t know anyone voting for Hillary to be honest, and if they are, they haven’t told me,” he said. Trump’s “personal life has nothing to do with me. He wants the illegals out, I want the illegals out.”

Danny Paiva, 31, of Shirley, a Suffolk County police officer and Navy reservist who served in Afganistan, said he would be voting for the first time ever. “He backs police officers, he backs the military, he wants to change a lot of things that are wrong,” he said. While he thought the “Access Hollywood” tape was “bad,” he didn’t expect Trump to act like that in the White House, he said.

“If something makes me say, ‘Wow, that’s not who I’d want to be president,’ I’d change my mind,” he said. “But not yet.”