It is a festive family photo with seven broad smiles and a Christmas tree. But one other detail sets it apart: each member of the Massie family is brandishing a machine gun or military-style rifle.

The photo was tweeted last week by Thomas Massie, a Republican congressman from Kentucky, with the caption: “Merry Christmas! PS: Santa, please bring ammo.”

A few days earlier, a school shooting in Michigan left four teenagers dead and seven people injured after a 15-year-old student allegedly went on a rampage.

Massie’s post earned widespread condemnation but was also seen as indicative of a performative, provocative brand of Republican politics, calculated to go viral, “own the libs” – that is, provoke outrage on the left – and contribute to the outsized influence of supporters of Donald Trump.

“Here his family’s got guns under a Christmas tree just after four kids were killed,” said Elaine Kamarck, a former official in the Clinton administration. “The guy’s abominable but that’s what’s happening to the Republican party. They’re flat-out nuts. There’s a piece of the Republican party that now supports violence.”

Recent examples include Paul Gosar, a congressman from Arizona, posting an animated video that depicted him killing Democratic congresswoman Alexandria Ocasio-Cortez and attacking Joe Biden. All but two Republicans in the House refused to vote to censure him.

Last month, Congresswoman Lauren Boebert made anti-Muslim remarks about Ilhan Omar. Boebert claimed she and a member of her staff were taking a lift at the US Capitol when she saw an alarmed police officer running toward them. She said she turned to her left and spotted the Minnesota Democrat standing beside them.

“Well, she doesn’t have a backpack. We should be fine,” Boebert recalled saying, to laughter. “And I said, ‘Oh, look, the jihad squad decided to show up for work today.’”

Omar urged House leaders to discipline Boebert. But Kevin McCarthy, the Republican leader, downplayed the incident and defended Boebert, insisting she had apologised both publicly and personally.

Omar responded on CNN on Sunday: “McCarthy is a liar and a coward. He doesn’t have the ability to condemn the kind of bigoted Islamophobia and anti-Muslim rhetoric that are being trafficked by a member of his conference.”

She added: “This is who they are. And we have to be able to stand up to them. And we have to push them to reckon with the fact that their party right now is normalizing anti-Muslim bigotry.”

Such incendiary antics are set to continue on Tuesday when Gosar is joined by Marjorie Taylor Greene of Georgia, Louie Gohmert of Texas and Matt Gaetz of Florida at a press conference to decry the treatment of people arrested in connection with the 6 January attack on the US Capitol. Republican extremists have sought to portray the rioters as patriots.

Each tossing of a verbal grenade commands more airtime than moderate Republicans receive going about legislative business, ensuring that Trump loyalists continue to dominate the national conversation. Taylor Greene, appearing on rightwing ideologue Steve Bannon’s podcast, boasted recently: “We are not the fringe. We are the base of the party.”

Kamarck, a senior fellow at the Brookings Institution in Washington, pointed to the recent congressional testimony of Facebook whistleblower Frances Haugen, who described how the platform’s model rewards those who shout the loudest.

“What we know from the whistleblower at Facebook is that the more dramatic, the more outrageous the picture, the more it grabs you,” Kamarck said. “The more it’s violent, the more clicks it’ll get. That’s what their algorithms are trained to do.”

Massie’s gun fetish post now has more than 80,000 likes on Twitter.

Kamarck said: “This guy wants to solidify a base, get campaign contributions from pro-gun people. This is simply unforgivable. There’s just no way that the majority of Americans agree with this kind of rabid, pro-gun stance, even people who are hunters and pro-gun people.”

With historical trends suggesting Republicans will win back the House next year, McCarthy appears determined to become speaker, meaning he cannot afford to alienate Trump or the most radical members of his caucus.

Kamarck added: “Kevin McCarthy is just the lowest of the low. He has decided that he has to placate a base which is very dangerous, which is violent and calls people to commit violent acts, and we’ve never had anybody like that. Kevin McCarthy thinks if he can hold all these crazy people in his caucus, he can be speaker.”

The dangerous shift in Republican ranks was on display recently when Kyle Rittenhouse, who was 17 when he killed two people at an anti-racism protest in Kenosha, Wisconsin, argued that he acted in self-defence and was acquitted on all charges.

Rittenhouse was invited to Trump’s estate in Florida, elevated to heroic status by rightwing media and feted by Republicans. Taylor Greene even sponsored a bill to award him a congressional gold medal.

Larry Jacobs, director of the Center for the Study of Politics and Governance at the University of Minnesota, said: “Within the Republican party, there’s a battle for leverage in terms of winning primaries and influencing primaries. Then you’ve got Donald Trump.

“He’s sitting there as a kind of monarch waiting for his subjects to come and pledge their fealty to him and one way to do it is to be the tough man to promise to take to the barricades to defend the 2020 election results, as Donald Trump sees it.”

He added: “We’re into the kind of outrage culture in the Republican party. There’s almost a competition as to who can be more outrageous, more vicious and threatening. It’s a race to the bottom.

“It’s a completely bonkers political party. This is one of the most dysfunctional and dangerous political parties in the democratic world. You’ve got Hungary, you’ve got Austria. There are places where you’ve had a surge on the right and I would say this is comparable. And maybe even a further extreme, if you look at what elected members of the US Congress are saying and doing.”