Republican rebel Liz Cheney braced Tuesday to lose her seat in the US Congress to an election conspiracy theorist, in the latest sign of her party's break with traditional conservatism to embrace Donald Trump's hardline "America First" agenda.

Once considered Republican royalty, the lawmaker from Wyoming has become a pariah in the party over her role on the congressional panel investigating the January 6 assault on the US Capitol -- and Trump's role in fanning the flames.

All eyes are on the primary in Wyoming, where defeat for the 56-year-old elder daughter of former vice president Dick Cheney would mark the end of the family's four-decade political association with one of America's most conservative states.

Even her loyal backers have privately accepted that Cheney will likely lose the Republican nomination for November's midterms to 59-year-old lawyer Harriet Hageman -- Trump's hand-picked candidate who has amplified his false claims of a "rigged" 2020 election.

The latest survey from the local Casper Star-Tribune has Cheney with just 30 percent support compared with 52 percent for Hageman, reflecting all recent polling.

Yet there is already speculation that Cheney may challenge Trump for the Republican presidential nomination in 2024 -- or even run as an independent -- and insiders are expecting her to deliver a concession speech that will double up as the launchpad for her political future.

"No matter how long we must fight, this is a battle we will win," she said in a video message posted before the weekend.

"Millions of Americans across our nation -- Republicans, Democrats, independents -- stand united in the cause of freedom."

Cheney has framed her campaign as a battle for the soul of a party she is trying to save from the anti-constitutional forces of Trumpism.

She is the last of 10 Republicans in the House of Representatives who backed Trump's second impeachment to face primary voters.

Four retired rather than seek reelection, three lost to Trump-backed opponents, and only two -- California's David Valadao and Dan Newhouse of Washington state -- have made it through to November's midterm elections.

Cheney, a tax-cutting, gun-loving right-winger, voted in line with Trump's positions 93 percent of the time when he was president but that hasn't blunted his retaliation for her role in the House committee probe.

Trump has made Cheney his bete noire, calling her "disloyal" and a "warmonger," prompting death threats that have forced her to travel with a police escort.

The blonde, bespectacled former attorney has been made persona non grata by the Wyoming Republican Party, whose chairman himself participated in the protests on the day of the US Capitol assault.

In her state -- the first to grant women the right to vote, in 1869 -- the congresswoman has been forced to run a kind of shadow campaign, with no rallies or public events.

She even avoided the traditional election day photo op Tuesday, eschewing media at her local polling station to instead cast her ballot in nearby Jackson.

"Liz is representing the constituents that are in her mind, and they aren't the constituents of Wyoming," said Mary Martin, chairwoman of the Republican Party in Teton County -- Cheney's Wyoming base.

Leaning on his red motorcycle, Bill Gonzales, 59, is one of the few voters who spoke to AFP in Cheyenne to defend Cheney's record, saying she "has stood up for what is proper within the country."

There are also elections on Tuesday in Alaska, where 2008 Republican vice presidential candidate Sarah Palin's comeback battle -- to complete the term of a congressman who died in office -- is dividing locals.

Fourteen years after rising to international fame on the losing Republican presidential ticket headed by John McCain, Palin remains popular among women as the "soccer mom" who pioneered the ultra-conservative "Tea Party" movement that paved the way for Trumpism.

But many voters blame her for abandoning her single term as governor halfway through, amid ethics complaints, and a recent poll showed her to be viewed unfavourably by 60 percent of Alaskans. (AFP)