The potential pairing of Mr. Trump and union members could be helped along by a sense that Mr. 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, the president of a building and construction trades council in northern New Jersey. “He’s done that in Manhattan, in New Jersey.”

But that is 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.)

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

Even more important for many union members has been the issue of economic globalization. Mr. 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 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. Mr. Leenders, who estimated that one-quarter to one-third of his factory’s union workers were Trump supporters, said he voted for Mr. Obama in 2008 and wrote in Ron Paul in 2012.