Top Trump targets Cheney, Murkowski, face voters in Tuesday’s primaries in Wyoming, Alaska

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Polls have closed in Wyoming, where Rep. Liz Cheney of Wyoming sits high atop former President Trump’s Republican hit list.

As Alaska, where Sen. Lisa Murkowski also attracted Trump's ire, and Wyoming hold primary elections on Tuesday, both federal lawmakers face voters for the first time since moving early last year to impeach Trump for his role in inciting the Jan. 6, 2021, storming of the U.S. Capitol.

While Cheney faces what public opinion polls suggest is near-certain defeat in her bid for a fourth two-year term representing Wyoming’s at-large House seat, Murkowski is all but certain to pass her first hurdle and advance to November’s general election. 

Also in the spotlight in Tuesday’s contests – former Alaska Gov. Sarah Palin - as the 2008 GOP vice presidential nominee and one-time darling of the right seeks to fill a vacant House seat.

CHENEY, FACING NEAR CERTAIN DEFEAT IN WYOMING GOP PRIMARY, EYES BIGGER BATTLE AHEAD

Rep. Liz Cheney talks with voters at Wyoming's Wind River Reservation, on July 16, 2022 (Liz Cheney re-election campaign?)

Cheney was the most senior of the 10 House Republicans who voted to impeach the then-president on a charge of inciting the deadly attack on the Capitol, which was waged by right-wing extremists and other Trump supporters who aimed to disrupt congressional certification of President Biden’s Electoral College victory in the 2020 election.

The conservative lawmaker and defense hawk immediately came under verbal attack from Trump and his allies, and in May of last year, she was ousted from her number-three House GOP leadership position.

TRUMP BLASTED BY DICK CHENEY AS FORMER VICE PRESIDENT STARS IN DAUGHTER'S CAMPAIGN COMMERCIAL

Cheney has been vocal in emphasizing the importance of defending the nation's democratic process and of putting country before party, and is one of only two Republicans serving on a special select committee organized by House Democrats that is investigating the riot at the Capitol. The committee has made headlines and grabbed plenty of national attention this summer as it has held televised hearings.

Trump, stepping up his efforts to oust Cheney from Congress, endorsed Harriet Hageman as she entered the Wyoming race last summer. The former president and his allies successfully urged some, but not all, of the other anti-Cheney candidates to drop out of the primary and coalesce around Hageman. The latest polls have indicated Cheney likely will get trounced on Tuesday by Hageman in a state where Trump won a whopping 70% of the vote in 2020.

Republican congressional candidate Harriet Hageman campaigns at the Goshen County Fair parade, in Torrington, Wyoming on August 4, 2022 (Hageman congressional campaign)

However, Cheney — in comments made in recent weeks — seems to be at peace that the likely primary outcome is a price she has to pay in order to achieve success in her bigger fight against Trump.

"I am working hard to earn every single vote," Cheney said in an interview on "Fox News Sunday" late last month. She emphasized, "Given the choice between maintaining my seat in the House of Representatives on the one hand or ensuring the survival of our constitutional republic and ensuring the American people know the truth about Donald Trump, I will choose the Constitution and the truth every day of the week and twice on Sunday."

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Cheney, in her closing video to Wyoming voters, took aim at her primary challenger's strong support for Trump’s repeated unproven claims that his 2020 ballot box loss to Biden was due to "massive voter fraud" and a "rigged" and "stolen" election.

"Like many candidates across this country, my opponents in Wyoming have said that the 2020 election was rigged and stolen. No one who understands our nation's laws, no one with an honest, honorable, genuine commitment to our Constitution would say that. It is a cancer that threatens our great Republic," Cheney argued.

Hageman, who got a boost when Trump held a rally on her behalf in Wyoming in late May, has repeatedly charged that "Liz Cheney has long forgotten she works for Wyoming, not the Radical Democrats. Wyoming deserves a Congresswoman who will represent us AND our conservative values. It's time to retire elitist Liz Cheney."

WYOMING 2022 PRIMARY RESULTS

Cheney is likely concession speech on Tuesday night will be closely watched by political analysts, for signs that her crusade against Trump could transform in a potential run for the 2024 Republican presidential nomination.

Of the 10 House Republicans who voted to impeach Trump, four decided against seeking another term in Congress. Of the six who ran for re-election, three have been defeated in GOP primaries, with two others advancing to November thanks in part to running in non-partisan primaries where the top two finishers advanced regardless of party affiliation.

Seven Senate Republicans joined all 50 Democrats in voting to convict Trump in the February 2021 Senate impeachment trial, where he was acquitted. Of those seven, Alaska's Murkowski is the only one running for re-election this year.

GOP Sen. Lisa Murkowski ?takes a picture with supporters in Talkeetna, Alaska on August 13, 2022. (Lisa Murkowski re-election campaign)

Murkowski’s call for Trump to resign following the Capitol attack and her vote to convict Trump on charges he incited the attack were not the first times she has raised his ire. The senator voted against a Republican-backed plan in 2017 to repeal the national health care law known as ObamaCare, and a year later she opposed confirmation of now-Supreme Court Justice Brett Kavanaugh, whom Trump had nominated.

ALASKA 2022 PRIMARY RESULTS

Trump repeatedly targeted the senator, and last year he endorsed Murkowski’s GOP primary challenger, former Alaska commissioner of administration Kelly Tshibaka. Trump traveled to Alaska a month ago to headline a rally for Tshibaka.

Republican Senate candidate Kelly Tshibaka marches in the Bear Paw Parade in Eagle River, Alaska on July 16, 2022. (Kelly Tshibaka Senate campaign)

Unlike Cheney, Murkowski enjoys the backing of Senate GOP leadership. She is supported by the National Republican Senatorial Committee, the re-election arm of the Senate GOP, which has long helped Republican incumbents running for re-election. Powerful Senate GOP leader Sen. Mitch McConnell and his political team are supporting Murkowski, as is the McConnell-aligned Senate Leadership Fund, the top outsider super PAC backing Senate Republicans.

HEAD TO THE FOX NEWS ELECTIONS CENTER FOR THE LATEST PRIMARY RESULTS

Also helping Murkowski - Alaskans, in a ballot measure last year, changed how they run their elections. They scrapped party primaries and implemented a process where the top four vote-getters in a non-partisan primary will advance to the general election, where ranked-choice voting will be used to determine the winner.

Murkowski, who has never won a majority in her Senate election victories, is no stranger to difficult contests. After losing the GOP primary in 2010 to Tea Party-supported challenger Joe Miller, she launched a write-in campaign and successfully won the general election.

Murkowski told Fox News on Saturday she is confident "the people of Alaska will return me to the United States Senate." 

CLICK HERE FOR THE LATEST FOX NEWS REPORTING FROM THE CAMPAIGN TRAIL

During her interview, she argued that "the problem that we have is that Donald Trump, when he was in office, failed to uphold the Constitution of the United States. For me it’s pretty simple."

Tshibaka, taking aim at Murkowski, told Fox News on Sunday that "we need a senator who’s going to vote for what’s in the best interests of Alaska and not say one thing to us and then do the opposite in D.C."

Alaskans will also be voting on Tuesday in three-way special election to fill the seat left vacant by the March death of GOP Rep. Don Young, who was the chamber’s longest-serving member.

Republican U.S. House candidate and former Alaska Gov. Sarah Palin speaks as former President Trump looks on during a rally at Alaska Airlines Center on July 09, 2022 in Anchorage, Alaska. (Justin Sullivan/Getty Images, File)

Palin, who is backed by Trump, is facing off against Republican businessman Nick Begich and Democrat and tribal activist Mary Peltola. Palin placed first in the June primary, at 27%, followed by Begich at 19%.

The contest will be the first in Alaska to use ranked-choice voting. Under the system, voters are allowed to rank all candidates in order of preference on the ballot. If no candidate wins a majority, the last-place candidates are eliminated, and their supporters' votes are reallocated based on those voters' second-place choice. Maine, in 2018, was the first state to use ranked choice voting in a federal election.

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Palin, Begich, and Peltola, are also the front-runners in a simultaneous primary that will be held on Tuesday, in the race to serve the next two years in Congress.

Fox News’ Jonathan Hunt, Jon Rule and Jake Karalexis contributed to this report.