Does Wyoming want Liz Cheney to hang onto her House seat?

CHEYENNE, WYO. -- Perhaps no midterm primary is getting more attention than that of Wyoming Rep. Liz Cheney, whose race this week could be the highest-profile test yet of the voter backlash -- or lack thereof -- to a Republican participating on the House Jan. 6 committee and whether anti-Trump conservatives have a path forward within their own party.

On Tuesday, residents of the least populous state in the nation will hand down their answer. As it stands, Cheney's chances for reelection are slim: Her opponent, Wyoming attorney Harriet Hageman, bests her in past head-to-head polling match-ups, according to FiveThirtyEight, helped in part by a blessing from former President Donald Trump. (FiveThirtyEight noted earlier this year that public polling on the race has been sparse.)

On Thursday, Cheney released an ad crystalizing her closing argument: The "big lie" about the 2020 election -- and Trump's embrace of it -- is ruining democracy.

Cheney called it "insidious."

"It preys on those who love their country," she said in the ad. "It is a door Donald Trump opened to manipulate Americans to abandon their principles, to sacrifice their freedom, to justify violence, to ignore the rulings of our courts and the rule of law."

Whether that pitch persuades enough of her party's base will soon be made clear. But interviews with approximately a dozen voters in Wyoming in recent days show they have other things on their mind.

Republicans in the state that Trump won with 70% of the vote told ABC News that they feel increasingly distant from their three-term congresswoman. And while they said they are unhappy with Cheney's prominent position on the Jan. 6 committee, which she vice-chairs, and her hardline stance against Trump's baseless election attacks, the Wyoming residents also said they felt she no longer represented them politically, either.

"After she jumped in on the Jan. 6 thing, and she jumped in on the impeachment, she was nowhere to be found. She wasn't meeting with the people. She doesn't care about us," Myrna Burgess told ABC at the Laramie County Fair.

"She's tone-deaf to even listening to us," said Burgess, also claiming that the congresswoman had taken a soft stance on Second Amendment rights because she like 13 other Republicans voted for a recent bipartisan anti-gun violence package. Burgess said that decision was another indicator that she's out of touch with voters.

"When she starts voting against the Second Amendment, that is a total dealbreaker," Burgess said.

Accusations that Cheney is mostly absent from the state have also been capitalized on by challenger Hageman.

"I am the only candidate that has traveled around this state," Hageman said at a recent event.

Cheney has been campaigning in Wyoming, as evidenced by photos shared by her team on social media, though she isn't holding wide-scale, big-tent events the way her opponent is. But that's because of concern for her safety after becoming one of the country's most visible anti-Trump Republicans, according to Wyoming state Rep. Landon Brown, a Cheney surrogate.

"She has to have private events that are not announced to the general public because of her safety. And that's a crying shame that somebody stood up for what they believed in in Congress, and they are now in a position where they have to worry about their safety and their family safety," Brown said.

Brown, like Cheney, said the race is about the existential choice facing the Republican Party: between embracing Trump's endless insistence the last presidential race was stolen from him -- or moving on.

In an interview with ABC News' Jonathan Karl last month, Cheney said her work highlighting Trump's attacks on elections was more important than being elected. But she said then that she was working to win.

"The single most important thing is protecting the nation from Donald Trump. And I think that that matters to us as Americans more than anything else, and that's why my work on the committee is so important," she told Karl.

"This is bigger than one person's presidency. This is our Constitution. This is our history. This is what we're going to be remembered for. And that's exactly what Liz is remembering. And there's a lot of people in my district alone, but as well as other people out there, that they feel the exact same way," Brown said. "And unfortunately, you know, everything lands in Wyoming's lap right now."

That's where Democrats are -- potentially -- coming in, in an unusual last-minute push to cross party lines to try and save an anti-Trump lawmaker who nonetheless had voted with Trump more than 90% of the time.

In Wyoming, voters can change party affiliations at relevant county clerk offices no later than 14 days before the primary election, or at polling locations on the day of the primary or general election. State law also allows voters to switch their party affiliations back for future elections.

That makes it theoretically easy for Wyoming Democrats to vote as Republicans in Tuesday's primary. Still, an analysis by FiveThirtyEight showed it's unlikely they'll make up the deficit with Republicans, given how many more conservatives there are in the state: 70% of voters in the state are registered with the GOP.

And in every midterm election in the past decade, more than 80% of primary votes cast have been for GOP candidates, meaning even those who haven't declared their party affiliation are more than likely to lean red.

Several Wyoming Democrats who turned on their own party and temporarily registered as Republicans told ABC News that they didn't make the choice lightly.

"The first time in my life I am a registered Republican," said Laramie resident Megan Hayes. "That gave me a little bit of a rash, but I did it and I already voted and I got an absentee ballot and I did vote for Liz Cheney,"

Language on the Cheney campaign website directs voters interested in crossing the aisle to the county clerk's office -- though the Cheney campaign rejects any notion that they are targeting Democrats specifically.

"I've never received these kinds of mailers and certainly not in this abundance for one race ever," said Connie Wilbert, a longtime Wyoming Democrat who has temporarily changed her voter registration status in order to vote for Cheney.

She said she's received stacks of mailers urging her to make the switch. Around her neighborhood, where she said mostly includes lifelong liberals, are swaths of Cheney yard signs.

"While I disagree with her on virtually everything else, all policies. I respect the heck out of because the taking this stand and I think it's really important," Wilbert said.

The Cheney campaign insists they aren't targeting Democrats, but said they'll welcome any support.

Behind much of the party-switching push is a group called Wyomingites Defending Freedom And Democracy, which last week even cut pro-Cheney ads with Democratic Reps. Tom Malinowski of New Jersey and Dean Phillips of Minnesota.

Their efforts may have begun to work: At least for a few thousand registered Democrats appear to have changed their registration over the past month, according to state elections data.

If -- somehow -- Tuesday's race ends up being close, that might be key.

"There aren't enough Democrats to ... sway this. If one candidate wins by 5,000 votes. Those Democrats who switched had no real sway," said Jim King, a political science professor at the University of Wyoming. "If the race was decided by 500 votes, well, then those people would have perhaps had an influence."