The congresswoman and daughter of former US vice-president Dick Cheney is all but certain to lose her seat to a Donald Trump-backed opponent in the Republican primary this Tuesday. But in swimming pointedly against the tide of MAGA mania, is she eyeing a much bigger political prize on the horizon?

Richard Young is a sprightly “ninetysomething” veteran. “I forget what comes after ninety,” he grins as he digs into his nightly supper of trout and vegetables at his local restaurant in Dubois, Wyoming, a picture-perfect town that appears to be entirely fashioned from wood.

Log cabins dot Dubois’s main street. Its pocket-sized downtown is straight out of an old Western. Wooden boardwalks etched with the names of its deceased were hammered down more than 100 ...