WASHINGTON >> Of all the voters who might be expected to resist the charms of Donald Trump, the 2 million members of the Service Employees International Union would most likely be near the top of the list.

The union, which endorsed Hillary Clinton in November, is widely regarded as one of the more progressive in the labor movement. It skews female and racially diverse — roughly the opposite of a Trump rally, in other words.

But in an interview, the union’s president, Mary Kay Henry, expressed concern that Trump holds appeal even for some of her members. “There is deep economic anxiety among our members and the people we’re trying to organize that I believe Donald Trump’s message is tapping into,” Henry said.

In expressing her concern, Henry reflected a different form of anxiety that is weighing on some union leaders and Democratic operatives: their fear that Trump, if not effectively countered, may draw an unusually large number of union voters in a possible general election matchup. This could, in turn, give Republicans a boost in swing states like Ohio, Pennsylvania, Michigan and Wisconsin, all of which President Barack Obama won twice.

The source of the attraction to Trump, say union members and leaders, is manifold: the candidate’s unapologetically populist positions on certain economic issues, particularly trade; a frustration with the impotence of conventional politicians; and above all, a sense that he rejects the norms of Washington discourse.

“They feel he’s the one guy who’s saying what’s on people’s minds,” Thomas Hanify, president of the Indiana state firefighters union, said of his rank and file.

Hanify said Trump has so far dominated the “firehouse chatter” in his state. While he allowed that his members tilt Republican, he estimated that most followed the lead of the union’s international leadership and supported Obama in 2008 and 2012.

Henry and other labor leaders remain confident that they can keep their members in the fold by making a case that the Republican Party’s economic agenda, including Trump’s, runs counter to the interests of working people. But they also see Trump as posing particular risks.

“Anyone who talks about dividing people in the country as a solution is a threat to the country, to democracy, the economy, and to working people, and we take every one of those seriously,” said Richard L. Trumka, president of the AFL-CIO.

The potential pairing of Trump and union members could be helped along by a sense that Trump, unlike more conventional Republicans, has historically enjoyed a cordial relationship with labor on many of his real estate projects.

“He has put his fair share into hiring union people,” said Richard Sabato, president of a building and construction trades council in northern New Jersey. “He’s done that in Manhattan, in New Jersey.”

But that’s not always the case. The owners of Trump International Hotel Las Vegas filed objections to a recent vote by roughly 500 of its workers to unionize, and the National Labor Relations Board has found merit to the claims that the hotel violated workers’ labor rights. (The Trump campaign did not respond to requests for comment.)

Sabato said his members, who lean Republican but in many cases voted for Obama, would “march behind” Trump on the issue of illegal immigration.

Even more important for many union members has been the issue of economic globalization. Trump has railed against the Trans-Pacific Partnership, the 12-country trade deal the administration finished negotiating last year. And he has bemoaned the administration’s failure to stand up to what he and many union members see as China’s mercantilist policies.

He has also fulminated against plans by the company that owns Nabisco to shift some production to Mexico — “I love Oreos,” he said, “I will never eat them again” — and vowed to impose a punishing tariff on imports of Ford cars unless the company canceled a $2.5 billion investment in new plants in that country.

“We like that he does not support TPP, that he has taken the position that there should be trade tariffs for a company that moves jobs overseas,” said Ryan Leenders, 30, a member of the International Association of Machinists in Washington state. Leenders, who estimated that one-quarter to one-third of his factory’s union workers were Trump supporters, said he voted for Obama in 2008 and wrote in Ron Paul in 2012.

Reflecting the anti-establishment mood that has engulfed parts of the labor movement, Leenders said he believed that more than half of his union’s workers support Sen. Bernie Sanders, while very few support Clinton, despite the fact that the machinists union endorsed her last summer. (A machinists spokesman said, “At this point, any estimates of support for a candidate are more a passing snapshot of popularity.”)

Many union officials are grappling with a similar dynamic, including the Teamsters, whose members have a “Teamsters for Trump” Facebook page, with more than 650 likes.

John Bulgaro, president of Teamsters Local 294 in Albany, New York, said Trump had generated excitement among his members, but that “a lot of people like Bernie Sanders.” He cautioned that they would need to hear more about Trump’s position on labor rights.

To be sure, polling of union voters shows that Clinton remains broadly popular and would carry most Sanders supporters in a matchup against Trump. But the same polling suggests that Trump could perform unusually well among these voters for a Republican nominee.

Christopher M. Shelton, president of the Communications Workers of America, which endorsed Sanders in December, said that while polling of his members showed Trump’s support lagging far behind support for Sanders and Clinton, it was higher than Republican presidential candidates typically net.

Despite Trump’s appeal, particularly among white working-class men, longtime labor officials and political operatives point out that Trump’s popularity before a single primary vote has been cast is a vastly different proposition than whether he would be able to retain that support in the fall.

“In every election around this time there are stories suggesting that union members will defect — ‘Oh, white union men won’t vote for Obama,’” Steve Rosenthal, a former political director of the AFL-CIO and progressive political organizer, wrote in an email response to questions.

In the end, Rosenthal said, union voters almost always end up voting overwhelmingly Democratic. White male union members favored Obama in 2008, and John Kerry in 2004, by roughly 20 percentage points, according to polling commissioned by the AFL-CIO, even as white men overall favored the Republican candidate by a large margin.

Rosenthal said that unions have proved adept at building support among their members for Democratic nominees that generally embrace their economic agenda and at undermining support for Republicans.

In a recent study of working-class voters in Ohio and Pennsylvania based on over 1,500 interviews, Working America, a labor-affiliated group, found considerable support for Trump among Democrats. But Matt Morrison, the group’s deputy director, said many Trump supporters were receptive to information that suggested a gap between the candidate’s words and deeds.

“Just delivering a little bit of new information, we could see that his brand takes a hit,” Morrison said, referring to reports that Trump may have used undocumented workers on some of his development projects.

Other experts cautioned that even if Trump does retain substantial support among white male union members without college degrees, that will not necessarily yield him an electoral advantage in November if he becomes the Republican nominee.

The voters that labor unions must typically work the hardest to turn out, like younger voters and Latinos, “are groups that will be highly motivated” against Trump, said Guy Molyneux, a pollster who has surveyed union voters extensively over the years. “That could produce net votes for the Democratic nominee.”

Molyneux also said that many of the union voters attracted by Trump were among the 30 percent of union voters who already vote reliably Republican.

Still, unlike most other Republicans, whose appeal to union voters rarely extends beyond cultural issues like gun rights, Trump’s economic pronouncements have a greater potential to scramble the standard political calculus.

“I do think that Trump is a threat,” said Mike Lux, a progressive activist who is a former labor official and veteran of President Bill Clinton’s administration. “If the Democratic nominee is Hillary, and she’s mushy at all on the trade issue, Trump will take that issue and drive it and drive it and drive it.”

© 2016 The New York Times Company