In Alaska and Wyoming primaries, 2 Trump critics could meet different fates as Palin eyes a comeback

Tuesday's primaries in Alaska and Wyoming will spotlight two big Republican detractors of former President Donald Trump -- and now two big targets of his revenge tour this election cycle.

The incumbents, Sen. Lisa Murkowski and Rep. Liz Cheney, may also see two diverging results at the ballot box.

Polls close in Alaska at 1 a.m. ET on Wednesday and in Wyoming at 9 p.m. ET on Tuesday.

Cheney learns her fate

Wyoming is the state that handed Trump his widest margin of victory in the 2020 election.

Cheney, Wyoming's lone member of the House, has since cemented herself as the one of the most vocal anti-Trump members of Congress.

She earned the ire of Trump, his ardent supporters and many of her fellow Republican lawmakers after she crossed party lines -- with nine other House Republicans -- to impeach him after the attack on the U.S. Capitol last year.

She was censured one month later by the Wyoming Republican Party and, though she initially survived a leadership vote among the House GOP caucus, she was subsequently booted from her position as the No. 3 House Republican.

Legislatively, Cheney and Trump were not political foes: As noted by FiveThirtyEight, Cheney voted with him on the issues 92.9% of the time.

But she has broken with Trump on what she calls the greatest issue of all: His continued, baseless attacks on elections. As vice chair of the House Jan. 6 committee, she has taken a major role in a year-long investigation into Trump's conduct before, during and after the Jan. 6 insurrection.

Cheney is the last of six House Republican incumbents to seek reelection after their impeachment vote last year. So far only two -- Rep. David Valadao of California and Rep. Dan Newhouse of Washington -- have successfully fended off their primary challengers.

The other three -- Reps. Jaime Herrera Beutler of Washington, Peter Meijer of Michigan and Tom Rice of South Carolina -- all lost to Trump-endorsed challengers. Cheney's chances of reelection also seem slim, according to polling cited by FiveThirtyEight, though surveys of the race are sparse and Cheney insists she still has a shot.

Cheney's main opponent is boosted by Trump: Attorney Harriet Hageman is a former Republican National Committee member -- and a former Cheney ally and Trump critic.

Once an adviser to Cheney in Cheney's short-lived 2014 Senate campaign, Hageman won Trump's approval in September 2021 and has since embraced his false messaging about the last presidential race, claiming that it was "absolutely" rigged.

Hageman, her supporters will say, also has a home-field advantage over Cheney: She is a lifelong Wyomingite while Cheney -- whose father held Wyoming's House seat for a decade in the '70s and '80s -- was raised in both Wyoming and the Washington, D.C., area. before she went on to work in national politics.

Hageman ran for Wyoming governor in 2018, pledging to "reform federal land management and access" in a state where nearly half of the land is federally owned. During that primary, she took the position of transferring federal public land to the states and suggested that 1 million acres of Wyoming be part of the pilot plan. The proposal raised eyebrows among leading conservation groups, most of whom endorsed Republican Mark Gordon, who went on to win.

Palin and Murkowski on the ballot

Further north, in Alaska, voters on Tuesday will be making a bit of history: The state has scrapped its party-line primaries in favor of a top-four system, where every candidate competes together, and has implemented a ranked-choice voting system for its general elections.

The special general election held Tuesday along with the primaries will be the first time Alaskan voters rank candidates on the ballot.

The new system works like this: If a candidate gets more than 50% of the votes, they win outright; otherwise, the last-place candidate is eliminated and their voters' ballots are distributed to the voters' second-choice picks. This process continues until a candidate gets more than 50%.

According to the new system's supporters, ranked-choice encourages more moderate candidates who can appeal to the most voters, especially in crowded fields.

One of the critics of the new system is also eyeing to win the special election to serve the few months remaining in late Rep. Don Young's term in the House. Former Alaska Gov. Sarah Palin, who is backed by Trump, seeks a return to elected office after running as the Republican vice-presidential nominee in 2008. Between then and now, Palin was a face of the Obama-era tea party movement -- a precursor, in style and substance, to Trump's platform -- and was a conservative pundit and TV personality.

She has called Alaska's new voting system a "convoluted" process that will result "in voter suppression."

Facing off against Palin are Nicholas Begich III -- Republican heir to a local Democratic dynasty whose family members include a former representative and state senator -- and Democrat Mary Peltola, a former Alaska state representative.

The polling aggregate from FiveThirtyEight shows Peltola doing well against both Begich and Palin. (The fourth candidate who advanced in the special primary, Al Gross, withdrew and urged people to back Peltola.)

The three are also the front-runners in the regular House primary election simultaneously being held Tuesday, in which 22 candidates are vying to advance to November's general election and secure a full two-year term in the House.

On the Senate side, incumbent Republican Lisa Murkowski faces her first major electoral test in years -- though, as history has shown, she is no stranger to surprising victories.

Murkowski is the only one of the seven GOP senators who voted to convict in Trump's impeachment trial last year to be on the ballot this year. Her vote, like Cheney's, led to a censure from her state's Republican Party.

Unlike Cheney, Murkowski has built a profile as one of the Senate's most moderate Republicans and repeatedly crosses political lines -- notably, supporting abortion access, voting against Trump-nominated Brett Kavanaugh's confirmation to the Supreme Court and negotiating last year's infrastructure spending bill.

Kelly Tshibaka, a former commissioner of the Alaska Department of Administration, hopes to unseat her. Backed by Trump, Tshibaka has cast doubts on the integrity of the 2020 election but ultimately recognized Joe Biden as the president. She also called last week's FBI search of Mar-a-Lago a "gross abuse of power."

According to FiveThirtyEight's polling aggregate, Murkowski and Tshibaka trade off the lead in various surveys.

Still, because of the primary's top-four rules, Murkowski is likely to advance from Tuesday to the general election. And even if she doesn't, she could still win: She famously lost the Republican primary in 2010 to tea party-challenger Joe Miller but went on to win the general election after more than 100,000 Alaskans voted for her as a write-in candidate -- in part, due to ads that taught voters how to correctly spell her name.

ABC News' Chris Donovan and Tracy Wholf contributed to this story.