What would a Liz Cheney run for president look like?

Rep. Liz Cheney, R-Wyo., has said for more than a year that she will do whatever it takes to keep former President Donald Trump from getting back into the White House.

That includes a potential run for president. And even if Cheney loses her congressional primary Tuesday to a Trump-backed challenger, as expected — or even if she pulls off a surprising win — a run for the nation’s highest office is likely to be her next mission.

But many questions would confront the Wyoming Republican — vice chair of the committee investigating the Jan. 6 Capitol riot, stalwart Trump critic and daughter of former Vice President Dick Cheney — if she did run for president. Would she do so as a Republican? As an independent? Or even as a Democrat?

And how would running for president in a Republican primary stop Trump? If the contest were run today, she would lose handily, given Trump’s enduring popularity with a sizable plurality of Republican voters.

Cheney herself is not talking about such speculation, but Republican political operatives who hail from the anti-Trump wing of the party told Yahoo News that a Cheney presidential run could have a two-stage strategy.

First, run in the GOP primary as the candidate for Republican voters who cannot stomach Trump and who want to vote their conscience. And then, run as a conservative independent in the general election, and try to hold on to as many of those voters as possible to deny Trump the votes he needs to defeat a Democrat.

“It’s a spoiler candidacy in that it's designed to prevent Trump from becoming president. It's designed to take from the GOP base and make it mathematically impossible for Trump to win,” Mike Madrid, a California Republican consultant, told Yahoo News.

“The purpose of a [presidential] primary is to build an operation to do just that,” he said.

Madrid said Cheney’s closing messages in the Wyoming congressional primary are the first step toward such a confrontation. Ads like the one she has run on Fox News recently, featuring her father, are “not an attempt to win Wyoming,” Madrid said.

“This is about a full frontal assault on the national Republican Party,” he said.

In the ad, Dick Cheney says that “in our nation's 246-year history, there has never been an individual who is a greater threat to our republic than Donald Trump."

"He is a coward. A real man wouldn't lie to his supporters. He lost his election and he lost big. I know it, he knows it and, deep down, I think most Republicans know it," the former vice president says. "There is nothing more important [Liz] will ever do than lead the effort to make sure Donald Trump is never again near the Oval Office."

A Cheney ally who asked to speak on the condition they not be named said the Wyoming primary is “the first battle in a much larger and longer war that she is going to win because the future of the country depends on it.”

“Regardless of what happens, she is going to be leading a broad coalition going forward to defend freedom and restore the principles that Donald Trump continues to undermine,” the Cheney ally told Yahoo News.

But the bigger question, again, is how.

Even if Cheney did mount a credible challenge to Trump in a Republican primary, gaining 10% or even 20% of the vote, how would she run in the general election as an independent without losing most of those voters back to Trump? Cheney’s biggest foes would be structural and psychological: a two-party system in which each side views the other as an existential threat.

The number of Americans who see members of the opposing political party as “more closed-minded, dishonest, immoral and unintelligent than other Americans” has increased significantly over the past several years, according to data from the Pew Research Center released last week.

Many Republicans who might support Cheney in a primary would be sorely tempted to snap back into voting for their party’s candidate in the fall election, simply to prevent the Democratic candidate from winning.

Such patterns are why democracy reformers promote changes to balloting such as ranked-choice voting, in which Americans would be able to support their first choice without fearing that they were indirectly helping a candidate they fear the most to win.

A handful of states and municipalities have begun to use ranked-choice voting in their elections. In Alaska, Sen. Lisa Murkowski, a Republican, is expected to retain her Senate seat this year because the state got rid of closed-party primaries. Instead, the top four vote getters of any party in Tuesday’s Alaska primary will advance to the fall election, which will be decided by ranked-choice voting.

Joel Searby, who was a senior adviser to Evan McMullin’s independent run for president in 2016 and is now involved in building a third political party called the Forward Party, said that “there's merit to the concept that a Liz Cheney candidacy would pull most from whomever the Republican nominee is.”

But Searby cautioned that “it's so early, so many things are going to happen,” and that it is likely there will be other independent candidates for president in 2024.

“I have heard from multiple credible sources that there are at least three incredibly wealthy individuals exploring independent runs,” Searby told Yahoo News. “It’s not going to be, if Liz runs, ‘There's your independent candidate!’ There is very likely to be a number of independent candidates.”

Any independent candidate would also have to confront the grueling reality of getting on the ballot in all 50 states. It’s a difficult, expensive and time-consuming process, and would likely be a clear early test of any grassroots enthusiasm for a Cheney presidential bid.

There would also be a risk, if Cheney ran as an independent, that she might siphon some votes away from the Democratic candidate, whether that is President Biden or someone else. Cheney might try to avoid that by emphasizing her conservative views on abortion, the economy and other matters.

But part of what has made her a national figure in this moment is the appeal she has built up among voters who are not just Republicans. “Cheney has this wider coalition that goes pretty deep into the progressives because they appreciate her courage,” Searby said.

If Cheney were to run as an independent, she would have to account for this risk, and reassure those who feared that her candidacy could actually help Trump win.

“If there were a scenario where running a third-party candidate or an independent would bolster Trump, I would not be a part of that,” Searby said.