The overflow crowd that gathered to see Representative Harriet M. Hageman at a civic center in Afton, Wyo., on Thursday evening included many of her longtime allies, but the pointed questions started even before she made it to the podium to begin speaking.

“Nobody is touching Social Security,” Ms. Hageman, a second-term Republican, told a retired woman sitting in the front row who blurted out her concerns about potential cuts to the program by the Trump administration.

Things got spicier from there.

The next evening, at another town hall about 100 miles south in Evanston, Scott Flint, a retired miner, confronted Ms. Hageman about how the Trump administration’s cuts had reached his pocket of the state, shuttering a local Mine Safety and Health Administration office that provides crucial support in the area.

President Trump and Elon Musk, he warned, would soon face the same problems that corporate employers do after mass layoffs.

“They come in with the chain saw and then they find out, ‘Oh, there was some value to what they were doing,’” Mr. Flint, 67, said later in an interview. “But those guys are gone. They’ve gone down the road. You’re not going to get them back.”