Senator Mitch McConnell of Kentucky, the majority leader, has suggested he could bring a gun control bill to the Senate floor, though the House Democrats’ move toward impeachment has slowed the momentum, for now. “Given the multiple horrendous shootings in August,” Mr. McConnell said last month, “we owe it to the American people to act.” This would force Ms. McSally to get on the record over an issue she has largely been able to avoid for years.

With many Democrats running for president talking openly about gun control after years of retreat on the issue, Mr. Kelly often finds himself fielding questions about their positions on the campaign trail.

His role as a high-profile gun control advocate with an intensely personal connection to the issue rivals his status as a former astronaut and combat veteran as his primary identity in the state, even as he tries mightily to broaden the aperture of his biography. He and Ms. Giffords co-founded Americans for Responsible Solutions, now called Giffords, a nonprofit and super PAC that promotes gun safety.

Recently, the head of the Arizona Republican Party, Kelli Ward, sent out a fund-raising note saying supporters needed to stop Mr. Kelly “dead in his tracks,” which stirred criticism. (Mr. Kelly sent his own fund-raising message to supporters highlighting the attack.)

“The fact that Mark Kelly’s wife is one of the most famous shooting victims here plays a role,” said Paul Bentz, a pollster and consultant here. But, Mr. Bentz added, “I just don’t think he wants to be defined by the issue.”

Ms. McSally, a retired fighter pilot and former House member who was appointed last year to fill out the late Senator John McCain’s term, has been evolving on her gun positions since the summer’s shootings, and as Mr. Trump has called vaguely for tougher gun laws.