Rep. Liz Cheney, defeated in Wyoming Republican primary, says "now the real work begins"

CBS News projects Rep. Liz Cheney, one of former President Donald Trump's fiercest critics, has lost the Wyoming Republican primary to Harriet Hageman, who was backed by Trump. And in Alaska, Sen. Lisa Murkowski and Trump-backed challenger Kelly Tshibaka were among the candidates advancing to the November general election.

In a concession speech Tuesday night, Cheney said she believed she could have won the primary but it required her to "go along with President Trump's lie about the 2020 election... That was a path I could not and would not take." 

"No House seat, no office in this land is more important than the principles that we are all sworn to protect. And I well understood the potential political consequences of abiding by my duty," Cheney said, before adding that she called Hageman to concede. 

"Now the real work begins," Cheney said.

"We must be very clear-eyed about the threat we face and about what is required to defeat it. I have said since Jan. 6, that I will do whatever it takes to ensure Donald Trump is never again anywhere near the Oval Office, and I mean it," she said.

She had told CBS News' Robert Costa on Tuesday before the polls closed that this primary is "certainly the beginning of a battle that is going to continue to go on." 

She looked beyond her congressional race to the battle she has been waging to hold Trump accountable for his efforts to overturn the 2020 election. "As a country, we're facing a moment where our democracy really is under attack and under threat," Cheney said. 

Cheney added that she has no regrets about the campaign she's run. "I feel very proud about all the work I've done together with the people of Wyoming over the last six years and really understand and recognize there's nothing more important than the defense of our Constitution." 

After Hageman was projected the winner, Trump congratulated her on Truth Social, calling her win "very decisive."

Cheney is the last of the 10 Republicans who voted to impeach Trump to face a primary challenge. Of those 10, only two have prevailed and will go on to the general election in November. Four have decided to retire or not run for reelection and three others have either lost to primary challengers or conceded. 

But Cheney, who once was the No. 3 Republican in House leadership and whose father is former Vice President Dick Cheney, has been one of Trump's most outspoken foes in the House. She is the vice chair of the House committee investigating the Jan. 6, 2021, attack on the U.S. Capitol and one of only two Republicans on the committee. 

The Wyoming Republican Party has both censured and disavowed her, a largely symbolic move. While House GOP leadership usually backs incumbents, House Minority Leader Kevin McCarthy has followed Trump's lead and backed Hageman.

Hageman was once a Trump critic and backed Sen. Ted Cruz in the 2016 election. But now she's embraced his support and his baseless claims that the 2020 election was stolen, allegations that have never been supported and that the House Jan. 6 committee has gone to great lengths to debunk. 

Cheney, whose national profile has risen during her crusade against the former president, has not shut the door on a presidential run in 2024. While some anti-Trump Republicans have acknowledged there is an open lane for a Republican like Cheney in 2024, she only polled at 2% in a recent Morning Consult poll on the 2024 primary.

CBS News projects that Sen. Lisa Murkowski of Alaska, another Trump foe, will advance to the general election. In Alaska's open-primary system, the top four vote-getters go on to the general election, and Trump-backed Kelly Tshibaka will also advance. The other two candidates have yet to be determined. 

Murkowski, who is also from a powerful political dynasty, has come back from the political graveyard before. First appointed to her seat in 2002 and then elected in 2004, Murkowski lost a primary challenge in 2010 but then became the first U.S. senator in over 50 years to win as a write-in candidate. She easily won reelection in 2016 and she has since become a Trump foe, including voting against Supreme Court justice Brett Kavanaugh in 2018.

The outcome of the special election race to finish the term of Rep. Don Young, who died in March is not yet known, and isn't expected to be finalized for several days or even weeks. Former vice presidential candidate and Gov. Sarah Palin, along with Republican Nick Begich and Democrat Mary Peltola advanced from the June primaries to Tuesday's election, but the counting continues in the multi-stage ranked-choice process, and absentee ballots may also be received until Aug. 26, though they must be postmarked by Aug. 16.

The three were also on the ballot in the primary for the regular election for Young's seat. CBS News projects that all three will all advance to the November general election. The fourth person on the ballot has yet to be determined, out of the 16 candidates.   

Ranked-choice voting will be used in the November elections for each of the Alaska races for governor, senator and congressional representative.