PRESCOTT, Ariz. — Martha McSally was speaking to a veterans group on Thursday about aggressive liberal politics when she suddenly shifted the conversation to Kyrsten Sinema, her Democratic opponent in the race for an open Senate seat here. “Speaking of treason,” she said, referring to Ms. Sinema, “her extreme views are out of step.”

It was a slightly awkward rejoinder. But it also appears to be Ms. McSally’s closing argument.

Ms. McSally, a Republican congresswoman, is employing an unusual tactic in the final stages of one of the most closely watched Senate races in the country, doubling down on a jarring claim she made in a debate this week: that Ms. Sinema’s response years ago to a radio host’s flip comment about joining the Taliban constituted a crime against the state.