Backlash referring to that war or anything else in the USA's prior history won't keep Liz Cheney from continuing to home in on deterioration of the GOP under Trump's reign. There's a big difference between what conservatives mean by a strong executive branch and the fascist-leaning brand of autocracy that Trump and his followers have pursued. And there's a big difference between a government lying to pitch a war and a president who lied 20k+ times on official matters in public, and who tried to go around corporations, Congress, courts and the Constitution whenever he could if they stood in his way-- all with apparent impunity, give or take a couple of impeachments not supported by more than a handful of his own party, and who then capped his career by inciting followers to try to keep him in office after he lost a re-election bid.
There was a (paywalled)
piece in the Boston Globe about the GOP's decision to "live and die with the Big Lie" that included some interesting remarks about Cheney and her background, from a former WH chief of Staff for Bush 43, Andy Card, and from a former Wyoming Senator, crusty ol' Alan Simpson
The piece also notes that Elise Stefanik has experienced a radical change of tactics since her earlier days in Congress when she was viewed as one of the more bipartisan-inclined Republican House members, and even distanced herself at first from Trump's ascension. Now she's his handmaiden in waiting, and yet there are plenty among her own party who doubt her credentials and even call her a liberal.
So bottom line the Republican Party is experiencing a set of fissures that in total seem to belie whatever are Kevin McCarthy's hopes for a "unified message" after the ouster of Liz Cheney from the #3 leadership spot in the House. He's not going to be able to paper this over as time goes on.