There was no more potent symbol of the government's detachment from the lives of the poor than Iain Duncan Smith's claim on Monday that he could live on £53 a week. This is the income to which some recipients of the social security system he oversees have been reduced.

Mr Duncan Smith, whose bedroom tax is forcing thousands of people out their homes on the grounds that they have one more room than they need, lives in the 17th-century Buckinghamshire manor his wife's family has owned for six generations. I don't know how many bedrooms it has, but according to the Mirror there's a swimming pool, a tennis court and five acres of gardens. It is, that paper says, part of a family estate which incorporates 1,300 acres of farmland and much of a village.

Duncan Smith did nothing to earn this good fortune, apart from marrying into inherited wealth. Yet he is deployed by the government to police Britain's poorest people, punishing those it calls "skivers" and rewarding those it calls "strivers".

His proposition seemed unlikely, and I thought it should be challenged. At noon on Monday, I tweeted, "So who's going to start the petition to get #IainDuncanSmith to prove he can live on £53/week – by doing it?"

One of the people who follows me on Twitter, Dom Aversano, suggested I write it myself. But I had a column to finish, so I threw the challenge back to him, while promising to tout it if he set it up. John Coventry of change.org joined our conversation: "We can help you promote and share too." By 12.45 Dom had written and launched a petition, calling on the secretary of state for work and pensions "to live on this budget for at least one year. This would help realise the Conservative party's current mantra that 'We are all in this together'. This would mean a 97% reduction in his current income, which is £1,581.02 a week or £225 a day after tax."

I tweeted it as soon as it was posted and began recruiting people with a lot of followers to publicise it. We watched as something extraordinary happened.

The first 1,000 signatures arrived in 23 minutes. The 10,000 mark was passed after three and a half hours. But it was still picking up speed. Within seven hours there were 50,000 signatures. In 11 hours, 100,000.

At the time of writing, the total stands at 350,000.

Change.org's John Coventry tells me: "The petition has been far and away the largest on Change.org since we launched in the UK. For a petition to grow at 9,000 signatures an hour is unprecedented … The previous fastest growing petition was started by Jimmy Wales and called for the Home Office to Stop the Extradition of Richard O'Dwyer to the USA. It had over 12,000 signers on the Sunday it was launched and reached a total of 253,000 signatures."

Unsurprisingly, Duncan Smith seems rattled. He angrily denounced our petition as "a complete stunt". This of course distinguishes it from the crowd-pleasing cruelties he is inflicting on the poorest, some of which save scarcely any money while wrecking the lives of thousands. If our petition is a stunt, at least it is a harmless one.

While I really would like to see Duncan Smith trying to live as he obliges others to live, I suppose you could call our petition a stunt, if you mean an act whose purpose is to draw attention to something. It highlights the hypocrisy of a government of millionaires which arraigns the profligacy of the poor. It dramatises the character of a government which, insulated by inherited wealth, accuses people living on a few pounds a day of suffering from a "culture of entitlement".

The work of 40 minutes has helped to force ministers, including, on Tuesday, the chancellor, on to the defensive. Now the story is no longer just about the feckless, greedy poor, the Daily Mail stereotype used to justify these vicious cuts. It's about the government's oblivious aristocrats, living in a world apart from those whose lives they toy with.