"What I'm trying to do... is to change the process so that we end up restructuring the culture so that people find that work always pays. It doesn't right now."
When asked if he could live on £53 a week, in response to a question posed by a working benefits claimant, Smith said: "If I had to I would."
Following the interview, a petition hosted on Change.org was set up, challenging the secretary of state to "prove his claim". By 18:00 BST on Monday, the number of signatories had reached more than 30,000.
Market trader David Bennett, 51, who works between 50 and 70 hours a week and earned around £2,700 last year, said his housing benefit had been cut from £75 a week to £57. His income works out at around £53 per week.
Respect For the Unemployed & Benefit Claimants hereby ask each group members to share & sign the following petition: Change.org
Speaking to the Today programme's John Humphrys, he explained that the reforms are "about holding back on the costs". He said that the government "is modernising the welfare system so that work always pays.
"Universal Credit means the poorest get the highest level of money, and that is the best way to deal with youth poverty, to deal with child poverty, and to deal with homes that are workless."
Listen to the 12 minute interview by clicking here: BBC Radio 4's Today programme
Cruel & vindictive government welfare cuts that come into force today will heap even more misery on Britain's poorest. The Conservatives & Liberal Democrats assault will hit millions of families, with low-paid workers, the unemployed and disabled people bearing the brunt.
The tax and benefit changes will leave families nearly £900 worse off on average according to the Institute for Fiscal Studies.
Meanwhile David Cameron and George Osborne are giving millionaires an average £100,000 tax cut."
The bedroom tax, changes to council tax benefit and the replacement of the disability living allowance will all have a devastating effect. It will disproportionately hit disabled people.
UK's poorest households face a bleak April as they struggle to budget for all these cuts coming at once. People are already cutting back on the essentials of food and heating but there is only so much they can do.
The result will be misery - cold rooms, longer queues at food banks, broken families, missed rent payments and yet more people facing homelessness - devastating for those directly affected, but bad for us all.
The Conservatives & Liberal Democrats in government are deliberately misusing evidence and statistics to misrepresent the plight of the poor, a report says.
The Methodist United Reformed Church, the Church of Scotland and the Baptist Union jointly published the The Lies We Tell Ourselves study - 'click here to download report'.
Researchers said evidence had been skewed to put the blame for poverty at the door of the poor themselves. The government said it had always made it clear that the system was failing people, not the other way around.
The churches said that a number of "myths" about welfare claimants have arisen as a result of statistics being misused. These are repeated by the media and find their way into the popular consciousness.
The myths, pin the blame for poverty directly on those who rely on welfare benefits while ignoring more complex reasons. These incorrect ideas must be challenged, according to Paul Morrison from the Methodist Church.
He said: "Everybody is complicit - politicians, the media and the general public.
"This is because we have a culture which allows us to tell lies in public life."
Mr Morrison said many people preferred to believe that bad things only happen to "bad people".
The report challenged several misleading ideas about welfare and poverty.
The Lies We Tell Ourselves study - 'click here to download report'.
Share & sign the following petition: Change.org
Respect For the Unemployed & Benefit Claimants
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