“It’s weird,” Alexandria Ocasio-Cortez mused on NBC’s Late Night with Seth Meyers earlier this month. “Why are so many grown men just obsessed with this, like, 29-year-old?”

Obsessed would seem to be the right word for conservatives regarding the progressive, provocative Democratic congresswoman from New York who is known as AOC.

Barely a speech went by at the recent Conservative Political Action Conference near Washington without a jaundiced reference to Ocasio-Cortez. There was even a cardboard cut-out of her next to a “Socialism Bread Line” at one of the event’s after-parties.

At Donald Trump’s rally in Grand Rapids, Michigan, this week, Donald Trump Jr described Ocasio-Cortez’s rise to prominence as “pretty scary”. The crowd chanted “AOC sucks!” with the kind of gusto usually reserved for another Democratic woman and Trump bete noire, Hillary Clinton, in the form of “Lock her up!”

Ocasio-Cortez is also the subject of a Republican attack ad in North Carolina’s third congressional district. Michelle Nix, a Republican, warned Ocasio-Cortez’s proposed Green New Deal would be bad for the locals.

“She has the media,” Nix said. “She has the followers. But bless her heart, she has some terrible ideas.”

Trump always needs a foil and she’s a very useful foil for him to say, ‘I’m running against radical socialists’ Charlie Sykes

In short, just as supporters have lionised AOC as the new face of the progressive movement, so the right has demonised her as the new face of socialism, a successor to Barack Obama, Clinton and Nancy Pelosi as the bogeyman or woman to rally the conservative base.

A recent Time magazine profile argued: “Wonder Woman of the left, Wicked Witch of the right. Ocasio-Cortez has become the second most talked-about politician in America, after the president of the United States.”

Time’s cover photo was a vivid sign of how quickly a phenomenon has formed. Charlie Sykes, a conservative commentator, said: “She looks like Evita. She’s obviously an exciting and charismatic figure, but I’m not sure she represents the direction that Democrats want to take in 2020.

“Republicans would love to make her the face the Democratic party. It’s from the Trump playbook: they would love to characterise the Democrats as this young, radical socialist from New York. To some extent, the Democrats are playing into their hands by elevating her. Instead of talking about members of Congress such as Abigail Spanberger and Conor Lamb in swing districts, we’re talking about AOC.”

Sykes, editor-in-chief at the Bulwark, added: “Trump always needs a foil and she’s a very useful foil for him to say: ‘I’m running against radical socialists.’ That’s exactly the way you’d build it up in the Trump White House.”

Ocasio-Cortez has duly emerged as an unwitting star of Fox News, the Rupert Murdoch-owned cable network where opinion hosts have shown devout support for Trump and a close relationship with the White House. When Trump gave a phone interview to close confidante Sean Hannity this week, his criticisms of the Green New Deal were accompanied by footage of Ocasio-Cortez, who has championed the proposal.

According to research for the Guardian by Media Matters for America, a not-for-profit that monitors coverage, Fox News mentioned – or played clips mentioning – Ocasio-Cortez 299 times over the past two weeks.

The freshman congresswoman has complained that the network “has turned into ‘AOC TMZ’”, referring to the celebrity gossip website. Hannity has described her as “the new leader of the Democratic party” who pushes “bizarre, far-left radical ideas”.

This is a millennial female minority, the three things the Fox News audience seem to fear the most Kurt Bardella

A Fox News spokesperson pointed to coverage in which hosts and anchors have invited the congresswoman on their shows and referred to her as “impressive”. In January she was interviewed as part of a report on healthcare reform.

The New York Post, also owned by Murdoch, recently published 24 articles about Ocasio-Cortez on its website in the space of six days, according to Vanity Fair.

Kurt Bardella, a former spokesperson and senior adviser for Republicans on the House oversight committee and ex-spokesperson for rightwing Breitbart News, said: “I think they’re looking for someone now that Hillary Clinton is gone from the day to day public eye.

“Here is someone who has become the most visible figure in Congress in a short space of time. She is bombastic. This is a millennial female minority, the three things the Fox News audience seem to fear the most. Whether it’s the travel ban or border emergency, she embodies the things that scare them.”

Alexandria Ocasio-Cortez talks to late-night host Seth Meyers. Photograph: NBC/NBCU Photo Bank via Getty Images

With 3.7m followers on Twitter, Instagram fame and several viral video clips, the youngest congresswoman ever elected has bigger name recognition than many Democrats running for president. She is therefore a more prized target.

Bardella, who has an article about Ocasio-Cortez pinned on his Twitter page, added: “We’re going to hear her name on the campaign trail as much if not more than the Democratic candidates. In their over-zealousness, Republicans are only serving to make her a more impactful and significant figure. I bet you AOC’s name ID on Fox News is absurdly high.”

Progressives believe the demonisation of Ocasio-Cortez is doomed to fail.

Neil Sroka, communications director for Democracy for America, said: “They are obsessed with AOC because she scares the hell out of them. She has electrified Democrats in a way we haven’t seen since Obama. There’s no doubt that’s part of the reason they’re going directly after her.

“She’s a young Latina woman advocating a sharp change in the policy trajectory of the country, and that’s horrifying for them. It’s everything they’re scared of. They think it will work for them in the long term and they can make her Nancy Pelosi II, but they’re going to lose that battle.

“They are only making AOC stronger. They have never had to confront someone who is committed to putting forward a bold agenda and doesn’t care about the criticism.”