Work and Pensions Secretary Iain Duncan Smith dismissed claims he was "slashing" welfare today - and insisted he could live on £53 a week.
He said he was making the system fairer and giving people the chance to "break free" of benefits.
Ministers launched a fightback as 660,000 social housing tenants deemed to have a spare room began to lose an average £14 a week in what critics have dubbed a "bedroom tax".
It is part of a package of significant welfare and tax changes coming into force this month, which opponents warn will hit poor families and the disabled particularly hard.
Changes to council tax benefit will see bills for an estimated 2.4 million households rise an average £138 a year, with two million paying for the first time, an anti-poverty group said.
The system has been handed to town halls to operate from today, but with 10% less funding.
On April 6, working-age benefits and tax credits will be cut in real terms with the first of three years of maximum 1% rises - well below the present rate of inflation.
Two days later, disability living allowance (DLA) begins to be replaced by the personal independence payment (PIP), which charities say will remove support from many people in real need.
And later in the month, trials begin in four London boroughs of a £500-a-week cap on any household's benefits, and of the new Universal Credit system.
Pilot schemes for the flagship scheme have been scaled back amid reports - denied by welfare officials - that IT problems have derailed preparations for its rollout from October.
Labour claims the impact of the measures and other coalition policies have left the average family almost £900 a year worse off.
Market trader David Bennett told BBC Radio 4's Today programme this morning that he earned around £2,700 last year working between 50 and 70 hours a week.
Mr Bennett said his housing benefit had been cut even though his children stayed with him several days a week, and that his overall income was now around £53 per week.
It was not clear why Mr Bennett was not receiving tax credits.
Mr Duncan Smith, whose ministerial salary is equivalent to around £1,600 a week after tax, stressed he did not know Mr Bennett's individual circumstances.
But asked whether he could live on £53 a week, the former army officer, who married into a wealthy family, replied: "If I had to I would."
During the course of the day more than 21,000 people signed a petition on the change.org website, calling for Mr Duncan Smith to "prove" he could survive on £53 a week.
The text urged him to "live on this budget for at least one year".
He insisted the Government was only trying to get welfare "back into order".
"We are in an economic mess," he said. "We inherited a problem where we simply do not have the money to spend on all the things people would like us to do.
"What I am trying to do is get this so we don't spend money on things that are unfair."
He urged critics to get the issue "in perspective", arguing that there was already no funding for extra rooms when people received housing benefit to rent privately.
"They are exactly the same group of people," he said. "The reality is taxpayers are subsidising people to live in these homes. They need to be reassured."
Mr Duncan Smith said the housing benefit bill had doubled in 10 years under Labour, and a quarter of a million people were living in overcrowded social housing.
"What I am trying to do is at least use the money we have got to be fair," he said.
"What we are trying to do is get control of the welfare bill... without actually slashing or attacking people; we are trying to reform and change it."
The Cabinet minister said his target was "restructuring the culture so that people always find that work pays".
"Full time work is where you break free of the welfare system. That is the critical element," he said.
"These reforms, yes they are about holding back on the costs. But really critically this government will look back, and people will say this is modernising a welfare system."
Writing in the Daily Telegraph, Mr Duncan Smith and Chancellor George Osborne said: "If you listened to the shrill voices of the Left you'd think that every change to the welfare system, and any attempt to save money, marks the beginning of the end of the world.
"In reality, we are just restoring the original principles of the welfare state: that those who can work must work, and a life on benefits must not be more attractive than working."
Shadow chancellor Ed Balls said that, according to the Institute of Fiscal Studies, the poorest 10% of households will lose an average of £127 under this year's changes, while the richest 10% will gain almost ten times that, or £1,265.
And families with children would be hit harder, Mr Balls said, with the poorest 10% losing £236 a year and the richest 10% gaining £3,654 a year.
"It's appalling, it's shocking, it's immoral, it's shameful, it's a disgrace, it's inhumane, it's just upside down," he told the Daily Mirror, adding: "The bedroom tax is possibly the worst, most cack-handed and massively unfair piece of policy-making I've ever seen."
Shadow work and pensions secretary Liam Byrne said answers to Freedom of Information requests from 37 local authorities showed a huge shortfall in smaller properties.
In total, 96,041 households faced losing benefit in the areas but there were only 3,688 one and two-bed homes available, they suggested.
The National Housing Federation, which represents housing associations, has warned the cut could actually increase the cost to the taxpayer if people are forced into private rented homes.
Mr Byrne said: "This wicked bedroom tax is going to rip neighbour from neighbour, force vulnerable people to food banks and loan sharks, and end up costing Britain more than it saves as tenants are forced to go homeless or move into the expensive private rented sector.
"It is the worst possible blend of cruelty and incompetence. The Government must think again and drop this tax now."