The Republican party is showing all the attention span of a hyperactive toddler this primary season, moving from one shiny toy to the next. Donald Trump still dominates the nursery, like some giant plastic fire engine. But the pieces are starting to look careworn and the battery is going on the siren. The former neurosurgeon Ben Carson, now tied with Trump in some polls, is the teddy bear dragged around the playground a few times and now slumped in a corner. Fresh out of the box though is Carly Fiorina, the former chief executive of Hewlett Packard, gleaming amidst the gaggle of tired rivals.

At the most recent Republican debate, Fiorina wore what seemed from podium height upwards to be an electric-blue wetsuit. She was the only candidate who didn’t look like she’d been living in hotels and breakfasting on doughnuts for three months. She shot down Donald Trump for questioning whether anyone could vote for ‘that face’ and the audience went wild. She is a conservative dynamo plucked from Cecil Parkinson’s most fevered imaginings. And a friend of Benjamin Netanyahu to boot. When she was in corporate technology sales, she once turned up to a meeting with socks stuffed down her underwear to show the men she had what it took to close a deal. She tells the story proudly in her memoirs. For rich, hot-blooded Republicans, how much better can you get?

But Fiorina might not be so attractive to middle America. She speaks with the brusque confidence of the corporate CEO, often starting sentences with the phrase, ‘I am angered by…’ She is angered by a lot: hypocrisy, the tax code, environmentalists and liberals, especially liberals. She says brutal things with a tilt of the head and a bright, white smile, the kind that evil executives put on when they are firing everyone, moving jobs to China and then leaving with a giant golden parachute.

For a lapsed Episcopalian who rarely goes to church, Fiorina is unusually angry about abortion. In the most recent candidates’ debate, she challenged the absent Hillary Clinton and Barack Obama to watch a video about government-funded abortion clinics gathering foetal tissue for medical research: ‘Watch a fully formed foetus on the table, its heart beating, its legs kicking, while someone says, “We have to keep it alive to harvest its brain.” ’ It’s the kind of gory stuff you hear on the anti-abortion, religious fringes, but not often in the mainstream.

She’s just as angry with anyone who fusses about climate change. She makes the usual conservative arguments that jobs matter more than the fate of animals, that the science on climate change is questionable and that there’s no point America putting its economy through the environmental wringer while China does nothing. But just when you’re thinking, ho-hum, another country-club Republican clinking the Scotch glass and grouching about tree-huggers, her anger takes her off piste. Wind turbines are an exciting technology, she said in a recent interview, but people need to know the truth: ‘Do we tell people the truth that it slaughters millions of birds every year? I mean, eagles, falcons, birds people that care about. Do we tell people that it’s slaughtering these birds?’

The greatest bird-slayer in America isn’t wind turbines. It’s windows. Followed by cats, high-tension wires, pesticides and then cars. Windmills aren’t butchering America’s birds of prey, spraying blood and feathers across the sky. Most of the birds who fly into them are ‘small passerines’, perching birds or songbirds. But the gore-crazed Fiorina wants us to think of environmental issues in the same way she wants us to think about reproductive rights, in the grisliest terms conceivable. Only the blood of eagles can sate her righteous anger.

But perhaps you have to use extreme language to get any attention in this primary circus. It works for Donald Trump, and Fiorina may be smart to use controversy to win media airtime. She also tells a mean personal story. Born to a solid middle-class family, started work as a secretary, rose to be head of the largest technology company in the world, survived breast cancer, buried a child. Tough. Resilient. Only in America.

Some of it is even true. Her father was an eminent judge who taught at Stanford Law School and served as deputy attorney general under President Nixon. She went to Stanford as an undergraduate, studied ancient Greek to read Aristotle and received a degree in medieval history and philosophy, which she jokes made her unemployable. She worked as a secretary in her university holidays and for six months in her early twenties. She then obtained an MBA and, at the age of 25, joined AT&T as a management trainee. Nineteen years later she was appointed chief executive of Hewlett-Packard, making her the most prominent woman in corporate America.

During her five-year stint at HP, she doubled the size of the company by acquiring a rival computer maker, Compaq, and was paid more than $100 million for her work. She managed through the collapse of the dotcom bubble, and HP emerged from the carnage in tolerable shape. But even today people still can’t agree whether she was any good. She was certainly ambitious, aggressive and brutal to anyone who opposed her. She was reported to have hung a painting of herself in the corporate headquarters, and issued noisemakers at corporate events to greet her when she arrived on stage. Her board fired her in 2005, citing problems with execution and a share price that had fallen 60 per cent under her tenure. She has not taken another job in business since.

In 2009 Fiorina was diagnosed with breast cancer; she underwent a double mastectomy, chemotherapy and radiation and has since recovered. That same year her 35-year-old stepdaughter, Lori Ann, died. Fiorina married her second husband, Frank, when she was 31. Frank had two daughters by his first marriage, who were ten and 14 at the time. The girls were placed in the custody of their mother, Frank’s ex-wife. As an adult, Lori Ann suffered from bulimia and became addicted to prescription drugs. She married, divorced and died having distanced herself from her father and stepmother. This was the child Fiorina tells her audiences she buried.

She derives emotional texture from this story, but she has never said enough about her relationship with her stepdaughter for her audience to empathise at more than the most superficial level. Lori Ann’s mother has said that Fiorina’s version of events is incomplete. This sounds like emotional dynamite which could still blow up in Fiorina’s face.

Many Republicans are now fantasising about unleashing Fiorina on Hillary Clinton. The only thing better than beating Hillary would be to gazump her bid to become America’s first woman president with one of their own. But Fiorina’s anger and attitude so far seem like the socks bulging through her underwear. Diverting and provocative, but not the real thing.