JACKSON, UNITED STATES (AFP) - Representative Liz Cheney, a vocal critic of Donald Trump, lost the Republican Party primary to run again for Congress to Harriet Hageman, a lawyer endorsed by the former president, NBC News projected on Tuesday (Aug 16).

Cheney, daughter of former vice-president Dick Cheney, has held the seat since 2017 but attracted Trump’s ire after voting for his impeachment last year and playing a leading role on the committee investigating the Jan 6, 2021 assault on the US.

Once considered Republican royalty, the lawmaker from Wyoming has become a pariah in the party over her role on the congressional panel pursuing Trump over the plot to overthrow the last election that culminated in the 2021 assault on the US Capitol.

Cheney’s defeat by Harriet Hageman marks a significant victory for the former president in his campaign to oust Republicans who backed impeaching him after a mob of his supporters stormed the Capitol building last year.

The fate of US Senator Lisa Murkowski of Alaska, who also voted in favor of impeachment and is facing off against another Trump-backed candidate on Tuesday, remains unclear. The polls for that primary, a nonpartisan format in which the top four vote-getters advance to the general election, have not yet closed.

With 18 per cent of the expected ballots counted, Hageman led the Republican field with 65.1 per cent of the vote, followed by Cheney with 30.3%, according to Edison Research.

Both Wyoming and Alaska are reliably Republican, making it unlikely that either’s result will influence whether President Joe Biden’s Democrats lose their razor-thin majorities in Congress. Republicans are expected to retake the House and also have a chance of winning control of the Senate.

The ousting of Cheney is nevertheless the latest sign of Trump’s enduring sway over the Republican Party. Trump, who has hinted that he will run for president in 2024, made ending Cheney’s congressional career a priority among the 10 House Republicans targeted for supporting his impeachment in 2021.

'We will win'

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 lower House of Representatives who backed Trump's second impeachment to be facing 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 per cent of the time when he was president but that has not 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.

Palin comeback bid

The blonde, bespectacled former attorney has also 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.

"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 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 govenor halfway through, amid ethics complaints, and a recent poll showed her to be viewed unfavourably by 60 per cent of Alaskans.