Iain Duncan Smith has dismissed claims he was "slashing" welfare - and insisted he could live on £53 a week.
The Work and Pensions Secretary 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 Monday, 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 begins to be replaced by the personal independence payment, 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.
Market trader David Bennett told BBC Radio 4's Today programme on Monday 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."
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."