Lindsey Graham’s moment, it seemed, came on the evening of Jan. 6. With crews still cleaning up the blood and broken glass left by the mob that just hours before had stormed the Capitol, he took the Senate floor to declare, “Count me out” and “Enough is enough.” Half a year later, a relaxed Mr. Graham, sitting in his Senate office behind a desk strewn with balled napkins and empty Coke Zero bottles, says he did not mean what almost everybody else thought he meant. “That was taken as, ‘I’m out, count me out,’ that somehow, you know, that I’m...