“T HE CHOICE isn’t what I’m breathing in, the choice is what I’m exhaling,” said Representative Alexandria Ocasio-Cortez, at a celebration of Martin Luther King Day in the Riverside Church in Manhattan this week. “And I think that the situation right now, with this administration, with the abdication of responsibility by so many powerful people—even people who abdicate that responsibility by calling themselves liberal or Democratic—I feel a need for all of us to breathe fire.”

The 29-year-old congresswoman’s many critics on the right are more concerned by what they think Ms Ocasio-Cortez may be smoking. Since her demolition of Joe Crowley, a moderate Democratic leader last year, in a primary bid for his safe Bronx-Queens district, she has become a hate-figure of seemingly limitless interest to conservative media outlets. (“Fox News debuts premium channel for 24-hour coverage of Alexandria Ocasio-Cortez” snarked the Onion, exaggerating only slightly.) Her rare combination of success and hard-left views is the ostensible reason. In the mould of her fellow democratic socialist, Bernie Sanders, on whose presidential campaign she worked, she is for universal Medicare, a federal job guarantee, making tertiary education free and forgiving college debt. Yet a relentless focus on Ms Ocasio-Cortez’s appearance, person and spirited behaviour suggests the vituperation is fuelled by darker forces than policy disagreement.

This makes the activist left, including many at the Riverside, a stage for civil-rights leaders including Martin Luther King through the ages, love her all the more. They also love the fire-breathing rhetoric she showed off in an on-stage chat with the author Ta-Nehisi Coates. Best of all they love her ability to sock it to her right-wing detractors, typically for the benefit of her 2.5m Twitter followers. “Don’t hate me cause you ain’t me, fellas,” she tweeted to House Republicans, after they booed her vote for Nancy Pelosi as Speaker.

That incident also exemplified the only way that Ms Ocasio-Cortez may actually matter. The right-wing hate-craze for her is fuelled by a fear that she could be about to turn America socialist. That rather under-rates the fact that freshmen House members have a long way to rise; that most of the new intake of Democrats are moderate (and many have had enough of her attention-grabbing); and that if their party ever did nominate a democratic socialist for president, she would be much likelier to keep America conservative. By far the biggest threat Ms Ocasio-Cortez represents is to her own party. Republicans ought really to love her for that.

The hard-left activist world she springs from mainly exists to shunt Democrats to the left. There are signs in the emerging Democratic presidential primary that it is succeeding. All three of the senators who have so far declared their candidacies—Kirsten Gillibrand, Kamala Harris and Elizabeth Warren—support Medicare-for-all, an idea that also sprang from Mr Sanders’s campaign. And Ms Harris and Mrs Warren have endorsed the concept of Ms Ocasio-Cortez’s signature proposal, the Green New Deal, a suite of policies to address both climate change and inequality.

Yet Ms Ocasio-Cortez wants to cause a much bigger shakeup on the left—as her on-stage reference to colleagues ducking their moral responsibility suggested. She celebrated her election last November by backing a campaign by Justice Democrats—an activist group founded by her chief-of-staff and fellow Sanders alumnus Saikat Chakrabarti—to unseat Democratic incumbents deemed insufficiently left-wing. She has since tried to make nice with the Democratic leadership, as her vote for Mrs Pelosi illustrated. “I do see my situation evolving—I take my oath of office very seriously,” she said at the Riverside. “I was giving myself a little more permission to be a little more out-of-pocket before my swearing in.” Yet keeping Ms Ocasio-Cortez sweet will be an important task for Mrs Pelosi, who has three decades more congressional experience but half a million fewer Twitter followers.

The veteran Speaker has made a decent start. But given that AOC , as the congresswoman is known, appears to have no interest in leadership positions or other plums within Mrs Pelosi’s gift, she will have to work harder. Indeed, the real challenge of Ms Ocasio-Cortez’s populist ideas—to both parties, but to the Democrats most urgently—is the way they expose the inadequacy of mainstream policy responses to the big problems, including inequality and global warming, she describes.

On climate, most obviously, Republicans have no basis to call her an extremist. Her diagnosis of the looming disaster is in line with scientific orthodoxy; theirs, a corporate-funded denial routine, is the outlier. Democratic leaders, by contrast, agree with her diagnosis of the problem. Yet they are alarmed by the profligacy of her proposals, which are based on an improbable ambition to decarbonise the energy sector by 2035. Their alarm is justified, yet it would carry more weight if they had more serious alternatives to offer. Republican denial of climate change has led to Democratic complacency on the issue. “This is our World War II,” Ms Ocasio-Cortez said at the Riverside. “And your biggest issue is how are we going to pay for it?” To check her left-wing enthusiasm, and perhaps save the planet, House Democrats need a better answer to that question.