Dick Cheney excoriates Trump in an ad for his daughter Liz Cheney.

A new advertisement for Representative Liz Cheney’s re-election campaign features a leader of a bygone era in the Republican Party excoriating the leader of the current one.

“In our nation’s 246-year history, there has never been an individual that was a greater threat to our republic than Donald Trump,” Ms. Cheney’s father, former Vice President Dick Cheney, said in the ad, released less than two weeks before Wyoming’s primary elections on Aug. 16.

He praised Ms. Cheney, who has become a pariah among Republicans for her criticism of Mr. Trump and her work as vice chairwoman of the House committee investigating the Jan. 6, 2021, attack on the Capitol, for “honoring her oath to the Constitution when so many in our party are too scared to do so.”

The one-minute ad landed with a bang Thursday on social media, where a single copy racked up seven million views. But in Wyoming, where Mr. Trump won 69.9 percent of the vote in 2020 — more than in any other state — it is highly unlikely to sway any significant number of voters in Ms. Cheney’s favor.

For decades before Mr. Trump transformed the party, Mr. Cheney was one of the most influential Republicans in the nation: He was the White House chief of staff under President Gerald Ford, secretary of defense under President George H.W. Bush and vice president under President George W. Bush, a position in which he wielded uncommon power and was an architect of the U.S. invasion of Iraq. But the Republican Party of 2022 bears little resemblance to the party he held power in.

At least six of the 10 House Republicans who voted to impeach Mr. Trump will be leaving Congress in January: Four of them are retiring and two were defeated in primaries, with another two still awaiting primary results several days after voting ended in Washington State. It would take an astonishing political turnaround for Ms. Cheney to avoid joining them. In a Casper Star-Tribune poll last month, she trailed her opponent, Harriet Hageman, by 22 percentage points.

In light of those numbers, the ad, like many of Ms. Cheney’s public statements as a leader of the Jan. 6 committee, seemed more of an appeal to history than one to the electorate.

Mr. Trump “tried to steal the last election using lies and violence to keep himself in power after the voters had rejected him,” Mr. Cheney said in the ad. “He’s a coward. A real man wouldn’t lie to his supporters. He lost his election and he lost big. I know it, he knows it, and, deep down, I think most Republicans know it.”

Of his daughter, he continued, “There is nothing more important she will ever do than lead the effort to make sure Donald Trump is never again near the Oval Office — and she will succeed.”