As Republicans head toward what could be a stalemated convention, they might recall how the party healed itself in 1952 in what was known as the “winter of discontent.” The Republicans drafted a military leader, Gen. Dwight D. Eisenhower, as their presidential candidate.

The looming showdown between Donald Trump and Ted Cruz is a potential “train wreck,” to quote my colleague Charles Krauthammer. Neither front-runner seems likely to have the 1,237 delegates needed for a first-ballot victory. If either ultimately prevails, the win could leave a residue of bitterness that could undermine the party’s chances in November.

How can the GOP escape this demolition derby? Some have proposed a unity bid by House Speaker Paul Ryan, or the redux of Mitt Romney. But these politicians would look like opportunists — stealing the nomination from the candidates who won most of the primaries and caucuses — and the result might be even more divisive.

Enter the candidates on horseback: It may sound like a crazy idea, but this country is hungry for the leadership the U.S. military, at its best, embodies.

Who should be on the roster of potential national-security draftees? Gen. James Mattis, a retired Marine who served as U.S. Central Command commander, has already been floated. The Daily Beast posted an item Saturday reporting that wealthy Republicans were urging him to consider a late candidacy.

Mattis is a blunt, plainspoken man who could rival Trump for impolitic comments. Four-star officers sometimes describe him as the “warrior monk” because of his intense, ascetic manner. But he’s a true leader, beloved by his troops, and an intellectual who keeps a volume of meditations by the Roman philosopher Marcus Aurelius, in Latin, by his bedside.

The GOP should consider some other names, if it’s looking for a former military leader who could unite a divided party and nation. A roll call, in alphabetical order:

— Gen. Stanley McChrystal commanded U.S. forces in Afghanistan and, before that, ran the deadly strike force known as the Joint Special Operations Command. Like Mattis, he’s a warrior who earned deep admiration from his subordinates. In retirement, he has been teaching international relations at Yale University and writing about leadership.

McChrystal might be controversial because he was sacked as commander in Afghanistan after a 2010 Rolling Stone article quoted him criticizing Vice President Joe Biden; critics argued that those remarks were unprofessional, but they probably wouldn’t bother grass-roots Republicans. McChrystal also helps lead a bipartisan group that advocates a new program of national service.

— Adm. Mike Mullen, former chairman of the Joint Chiefs of Staff, led the military into a new era of tolerance toward gay men and lesbians. That might not endear him to Republicans, but officers who served with Mullen say he had a rare ability to unite the military and represent it to the country. His manner is low-key and cannily reserved, a bit like that of Eisenhower, another officer with a knack for managing difficult personalities.

— Gen. David Petraeus, commander of U.S. troops in Iraq, Afghanistan and at Centcom, is probably the most decorated officer of his generation. Leading the surge of U.S. troops in Iraq in 2007, he managed to reverse the sectarian bloodbath there and briefly stabilize the country, in one of the few bright moments for the United States in Iraq.

Petraeus stumbled as CIA director when he shared classified information with a West Point graduate who had written his biography and with whom he was having an affair; he pleaded guilty to a misdemeanor charge. Since leaving the CIA in 2012, he has been working for an investment firm and teaching at Harvard University, the University of Southern California and the City University of New York.

— A final name would be former Rep. Mike Rogers, who retired in 2014 after heading the House Intelligence Committee. Rogers served only three years in the Army, but he makes the list because of his service as an FBI agent from 1988 to 1994 fighting organized crime in Chicago. Rogers also has a rare talent, among conservative Republicans, of working effectively with Democrats. He took a broken, divided intelligence committee and, by allying with the Democratic ranking member, made the panel work.

I tried to contact Mattis, McChrystal, Mullen, Petraeus and Rogers on Monday. But all of them either couldn’t be reached or declined comment. One virtue or liability of these names, depending on your perspective, is that except for Rogers, I’m not sure of their party affiliation.

The GOP may continue on its fun house ride with Trump and Cruz, but it is increasingly likely that this journey won’t have a happy ending. Maybe it is time for Republicans to consider a nominee who might actually be able to lead the country out of the wilderness.

By David Ignatius 

David Ignatius’ email address is davidignatius@washpost.com. — Ed.

(Washington Post Writers Group)