Now, Ted Pappageorge, the head of the immigrant-heavy Culinary Workers Local 226, said he was worried about Mr. Trump’s draconian promises to deport undocumented immigrants en masse and slam closed the U.S.-Mexican border.

Ms. Harris’s “messaging was on point,” he said. But what Mr. Trump was doing was tantamount to the efforts of a manager to undermine an organizing drive, he suggested, and he had significantly more time to do it.

“She had a couple of months to do that, and Trump has been banging away doing what we call ‘a boss campaign’ for years, introducing a massive amount of fear and division,” Mr. Pappageorge said.