Everett Eaton, a 58-year-old banker, had just finished lunch at the Portsmouth Rotary Club when he spoke with three longtime friends about Donald Trump. The quartet had heard Trump speak to their club in 1987, and Eaton, a Republican, said his opinion of the tycoon had only worsened.

“You’re voting for Hillary?” asked a startled fellow Rotarian who knew Eaton’s political leanings.

“I have to,” Eaton responded. “He’s an embarrassment.”

While Trump’s support from white men has been helping keep him close to Hillary Clinton in national polls and some battleground states amid a swirling controversy over his treatment of women, the Rotary Club conversation here illustrated why the GOP nominee faces a more difficult hurdle in New England — where surveys show he wins a far smaller share of white men than he does in other parts of the country. That could be significant for Trump, whose narrow path to victory probably requires New Hampshire’s four electoral-college votes, as well as at least one electoral vote from Maine, which divides its winnings by congressional district.

The Trump campaign hopes that New Hampshire is an Election Day fire wall. It was here that Trump made a comeback from his Iowa primary loss and began his march to the nomination. Clinton, meanwhile, lost here in the primary to Sen. Bernie Sanders (I-Vt.) by a stunning 22 points. Moreover, New Hampshire’s racial and ethnic makeup theoretically benefits Trump, with African Americans constituting only 1 percent of the population and Hispanics 3 percent. That increases the importance of the white male vote here.

But in recent days, as reports of Trump’s lewd comments and alleged groping continued to hurt his standing among women, they also threatened his thinner margin among men. Before those reports, Trump led in the South among white men by 37 percentage points, but his lead among the same group was only nine points in New England and 13 points in other northeastern states, according to a Washington Post-SurveyMonkey poll conducted in August.

[A 50-state poll shows exactly why Clinton holds the advantage over Trump]

All of that means Trump may have one of his slimmest margins for error here in New Hampshire, and the Clinton campaign is striving to slice the male margin further. That effort was on display Thursday, when first lady Michelle Obama delivered a fiery attack on Trump for his comments about women and highlighted the impact upon men. “Strong men — men who are truly role models — don’t need to put down women to make themselves feel powerful,” she said in Manchester.

Separately, Sen. Jeanne Shaheen, a Democrat who was the state’s first female governor, said the Clinton campaign is replicating the way she combated charges that she was not tough enough on foreign policy and defense. Those are subjects on which “men traditionally seem to be more engaged,” she said in an interview, adding that it will be important to remind such voters about the danger of “giving Trump the nuclear codes” and how Trump denigrated Sen. John McCain (R-Ariz.), who was held prisoner for five years in Vietnam, as “not a war hero.”

Shaheen embodies the dramatic rise in power among women in New Hampshire, one that Clinton hopes to capi­tal­ize on. The state’s governor, Maggie Hassan (D), and its two senators are women. By contrast, when Trump visited Portsmouth in 1987, it was relatively rare to find women in top political positions. Even at the Rotary Club where Trump spoke in 1987, there were only a dozen women out of 235 members, compared with 40 percent today, according to chapter records.

Notably, other than the presidential campaign, the highest-profile race here is the Senate contest between Hassan and the Republican incumbent, Sen. Kelly Ayotte. Trump’s controversial statements have long been a major issue in that race. Ayotte spent weeks agonizing how far to distance herself from her fellow Republican. At first, she said she would vote for Trump but not endorse him. Then, after The Post on Oct. 7 obtained the “Access Hollywood” video, in which Trump spoke about grabbing women’s genitals and being able to kiss women immediately because he was powerful, Ayotte declared that opposing Trump now “is more important than winning any election.”

Ayotte’s announcement could exacerbate Trump’s problems with maintaining support among women. The Post-SurveyMonkey poll found that Trump led in New Hampshire by 16 points among men but that Clinton led among women by 32 points — a gap that is expected to have grown in the wake of the “Access Hollywood” tape and allegations by several women that Trump groped them.

At the same time, some of Trump’s signature issues are less important in New Hampshire than elsewhere. Trump’s call for expelling 11 million illegal immigrants does not have the same resonance in a state that has only 15,000 undocumented residents, according to the Pew Research Center. The state’s unemployment rate is 3 percent, below the national average of 5 percent.

James Boyle, who owns the Toyota dealership in Portsmouth where Trump is slated to speak Saturday, said that the state is suffering and that the Republican’s message appeals to many voters. “No one is coming here to start their businesses,” he said. “We need someone from the outside” in the White House.

Predicting the outcome of the vote in this famously independent state is difficult. A wild card is the influence of the Libertarian Party ticket — former New Mexico governor Gary Johnson and former Massachusetts governor William Weld. The RealClearPolitics polling average has the Libertarian ticket with 8.3 percent support, one of its strongest showings.

It is well remembered here that the Green Party’s Ralph Nader received about 4 percent of the vote in 2000 in a contest in which George W. Bush beat Al Gore by one percentage point. If Gore had picked up 7,000 Nader votes, he could have won the state — and the presidency. While the Florida recount got most of the attention that year, it was New Hampshire’s four electoral votes that gave Bush his 271-to-266 margin of victory — which explains why both campaigns come here frequently.

The quartet of Rotarians who saw Trump speak to the club 29 years ago said they remembered the circuslike atmosphere and huge media presence. Trump sounded then much as he does today, saying the country faced “disaster,” but he stunned the audience at the time by declining to seek the presidency, even as he said New Hampshirites might one day “beg” him to do so.

Dave Holden, an independent who was at the 1987 gathering, said at Thursday’s club meeting that he considered Trump “an existential threat to our country.” He said he was familiar with polling elsewhere and was “amazed at the support he has among white males.”

The two others in the quartet were split: Bob “Tube” Loch, 65, a printer, said that Trump “has all kinds of problems” but that “I’m going to vote for him because, for the first time in my life, I want to see if an outsider can get in there, because he if can’t, that door is closed forever.” Andy Fleischer, 65, a commercial real estate broker, said he will not vote for Trump and would consider voting for a third-party candidate, but only if he was sure Trump would lose.

Barbara Miller, a banker who attended the Rotary meeting Thursday and heard the quartet talking about Trump, warned that it would be wrong to assume Clinton can count on female supporters to win. Miller said she is voting for Trump because of his conservative views regarding the Supreme Court and the military, and she echoed Trump’s attacks on Clinton.

“I don’t support Hillary one bit,” she said. “She lies, she should be prosecuted, and she should be in jail.” As for reports that Trump made lewd comments about women and allegedly groped several, she dismissed them. “I hear talk like that in bars and restaurants and TV and HBO all the time,” she said. “I don’t like it, I don’t think it is something that men should be saying, but if it is Hillary versus Donald Trump, I way prefer Donald Trump.”

Scott Clement contributed to this report.