I first met them at a Trump rally in October in the Western Pennsylvania town of Ambridge, once the vibrant headquarters of the American Bridge Company, where Mr. Paslow’s mother wound cables during World War II. Mr. Peterson proudly wore his Trump-Pence T-shirt; Mr. Paslow a more modest Trump sticker. They had both been out of work for more than a year, laid off from their jobs in oil and gas exploration with two weeks’ notice, no severance, no pension and no unemployment insurance — like many American workers, they were independent contractors, without the protections of full employment. And like many American men, they were now depending on their wives’ jobs to get by.

Image Joe Peterson, left, with Al Paslow at a Donald Trump campaign event in October in Ambridge, Pa.

Mr. Trump came striding into this bleak landscape and offered them hope. He pledged to the crowd that he would bring back the oil and gas industry the very first day he was in office. “Unbelievably, that is exactly what we wanted to hear!” Mr. Paslow said. “Our hearts were uplifted.”

What struck me that day and in conversations over the next several months was how much it meant to them to be heard and seen, and how durable their trust was, once conferred. Here was a celebrity self-proclaimed billionaire who was paying attention to their fate, their town, their battered industry. They are quick to suspect conspiracy and corruption, in their state and in Washington. They thought even Mr. Trump might have his price — but luckily, it would be too high for most to afford.

This amalgam of faith and cynicism still binds them to their president. They may not like his tweets — “bad,” Mr. Peterson said in his only criticism — but they consistently give him the benefit of the doubt.

They dismiss protesters as sore losers, and pundits who attack policy swings as establishment voices bent on sabotage. Where critics point to promises unfulfilled, they see obstacles that are not their president’s fault.