One of the less dignified spats in US politics rumbled onwards on Sunday, as the Wyoming Republican Liz Cheney responded to a bizarre insult from Donald Trump. “I like Republican presidents who win re-election,” Cheney tweeted, with a picture of George W Bush. Bush beat John Kerry for re-election in 2004. Cheney’s father, Dick Cheney, was vice-president to Bush. Liz Cheney’s tweet was a response to an image released by Trump on Thursday. Under the heading “ICYMI: Must-See Photo”, a Trump-affiliated political action committee sent out a photoshopped image which spliced Cheney and Bush. Trump displayed the image at a rally in Georgia on Saturday but he could not tweet it himself, as he remains barred from the platform for inciting the deadly assault on the US Capitol on 6 January. Trump was then 14 days away from ceding the Oval Office to Joe Biden, who denied him a second term with a convincing election win. Trump has not conceded defeat. At a rally near the White House on 6 January, Trump repeated lies about supposed electoral fraud and told supporters to “fight like hell” to overturn the result. Five people died in and around the ensuing invasion of Congress. More than 650 have been charged. Cheney was one of 10 House Republicans to vote for Trump’s impeachment over the attack – his second, unique among presidents – but because only seven Senate Republicans could be persuaded to vote to convict, Trump remains free to seek re-election. Only one president – Grover Cleveland, a 19th-century Democrat – has won the White House again after losing a re-election bid. Trump, however, remains the dominant force in the Republican party, staging rallies, repeating his lies about electoral fraud, handing out endorsements, attacking enemies within the party and without and presiding over a growing campaign war chest. The spliced Bush-Cheney image was accompanied with a link for donations. Cheney’s response was lauded on Twitter by Meghan McCain, another daughter of a Republican establishment figure attacked by Trump, in her case the late Arizona senator and presidential candidate John McCain. With Adam Kinzinger of Illinois, Cheney is one of two Republican members of the House select committee investigating the 6 January assault. On Thursday, it announced subpoenas for figures close to Trump including former chief of staff Mark Meadows, his deputy Dan Scavino and former White House strategist Steve Bannon. Cheney, a stringent conservative, is among Republicans opposed to Trump to have attracted primary challengers. Earlier this month she responded to Trump’s endorsement of Harriet Hageman, a Wyoming attorney, with another pithy tweet. “Here’s a sound bite for you,” she wrote. “Bring it.” An interview with Cheney was due to be broadcast by CBS 60 Minutes on Sunday night.