I have some history with the Cheney family because I met Richlard Cheney, the former Wyoming Congressman and vice president, back in 1994. I attended the Green Bay Rotary Club Free Enterprise Dinner, where Cheney spoke. I had a pleasant conversation with him for a couple minutes afterward, including our own UW–Madison connections (his doctoral studies and my bachelor’s degree).

Six years later, when George W. Bush got the Republican nomination for president, he picked Cheney to head his vice presidential search, which concluded with Bush picking … Cheney. Six interminable months later, when the 2000 presidential election finally ended, I could say that I knew the vice president. And for the next eight years, when Democrats cast Cheney as the Darth Vader to Bush’s Grand Moff Tarkin, I could say that I knew the secret president.

The one thing no one ever called Cheney was a RINO, which makes the whole kerfuffle over his daughter, U.S. Rep. Liz Cheney (R–Wyoming), who had a 92.9 percent Republican voting record, ironic to say the least. The Wall Street Journal seems the only media outlet capable of a measured, objective look at Liz Cheney:

Liz Cheney lost her Republican primary in Wyoming Tuesday because she bravely stood up to the stolen-election falsehoods of Donald Trump. Liz Cheney lost the primary because she alienated too many Republicans by making common cause with Democrats like Rep. Adam Schiff.

Both statements can be true, and in our view both explain why Ms. Cheney lost decisively in a conservative state that had elected her three times and sent her father to Congress more times than that.

Mr. Trump targeted Ms. Cheney for defeat as he did the other nine Republicans who voted to impeach him after his disgraceful behavior on Jan. 6, 2021. He now has his revenge, as eight of them have lost or retired from Congress, but Republicans shouldn’t be so pleased.

Ms. Cheney is a conservative by any measure and she has the courage of her convictions. A party that can’t tolerate Ms. Cheney and others for voting their consciences after the ransacking of the Capitol by a Trump-inspired mob is narrowing its political and moral appeal. She represents a not inconsiderable number of GOP voters who can’t abide Mr. Trump.

Yet we don’t believe most of the Republicans who voted for Ms. Cheney’s opponent were dismissing the riot as a mere political protest or cheering on Mr. Trump. They were rejecting the strategy of the Democrats and the media to tar the entire GOP as rioters and fanatics.

Ms. Cheney associated herself closely with that effort by her leadership role on the House Jan. 6 special committee. She didn’t publicly object when the committee leaked text messages of Ginni Thomas to attack her husband, Justice Clarence Thomas. She agreed to subpoena sitting Members of Congress in a gross breach of political norms.

She is also the leading committee voice urging the Justice Department to prosecute Mr. Trump as a criminal for his behavior that day, though the committee still hasn’t provided evidence that Mr. Trump had any direct ties to the rioters. You won’t persuade many Republican voters by calling their party “very sick,” as Ms. Cheney did in early August.

GOP voters can hate what happened on Jan. 6 but also dislike the tactics of a committee that excluded Republicans who might have cross-examined witnesses. We warned that Speaker Nancy Pelosi would hurt the credibility of the committee by blocking Minority Leader Kevin McCarthy’s appointees, and the public’s view of its work has predictably split along party lines. One result has been to cost Ms. Cheney her seat in Congress.

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Ms. Cheney’s concession speech suggests her mission in politics now is to prevent Mr. Trump from becoming President again. One option is running for the White House herself. She’d have little chance at the GOP nomination. But her goal may be to prosecute the political case against Mr. Trump in such a way that opens the door to other candidates.

If Mr. Trump is the GOP nominee, Ms. Cheney could attempt a third-party run, though she says she won’t change parties. Third parties haven’t won since Lincoln and the GOP in 1860, but Ross Perot arguably cost George H.W. Bush the White House in 1992.

All of this points to the problem Republicans continue to have as long as Mr. Trump is the dominant party figure. He is toxic to a majority of voters even as he retains the fervent support of tens of millions. That voter divide cost him re-election in 2020, as enough Republicans in key states voted GOP for Congress but Joe Biden for President. That evidence is clear in the county and Congressional district returns.

This is why Democrats are doing their best to put Mr. Trump front and center in the 2022 campaign—with the Jan. 6 committee extending into the fall, and the continuing civil and criminal investigations in Georgia, New York and Washington, D.C. Democrats may hate Mr. Trump but they also believe he will help them retain power despite their manifest policy and governance failures. Liz Cheney lost in Wyoming, but her revenge may be a divided GOP that loses again in 2024.

• US politics