The Government has said proposals to limit benefits will be implemented "in full" despite a House of Lords defeat backed by a record rebellion among Lib Dem peers.
Conservative Deputy Chairman Michael Fallon said: "Ed Miliband has fallen at the first hurdle and failed the key test of his leadership.
"He has promised to 'take the tough decisions' on reforming welfare. But his party in the Lords supported a wrecking amendment to ensure that some families get thousands of pounds more in benefits than the average family earns by working."
Enver Solomon, policy director at the Children's Society, said: "The Lords have stood up to the Government and sent a clear message in support of children up and down the country.
"Children should not be held responsible and penalised for the employment circumstances of their parents.
"The Government must not ignore the fact that the Lords have spoken out to defend the plight of some of the country's most disadvantaged children."
Gavin Poole, executive director at the Centre for Social Justice, a think tank set up by Mr Duncan Smith in 2004, said: "This result is peculiarly out of line with public opinion which shows that almost 80% were in support of the proposed cap.
"Britain has been gripped by a worklessness crisis for years - the number of households where no one has ever worked doubled since 1997, and two million children are growing up in workless households. Tonight members of the House of Lords failed to provide the leadership required to start reversing that failure."
Work and Pensions Secretary Iain Duncan Smith wants out-of-work payments limited to £26,000 a year per household, which he claims will save "something in the order" of £600 million towards deficit reduction.
But the plans have caused deep unease in the Lords and prompted Church of England bishops to launch a bid for the reforms to be curbed, which was backed by a majority of 15.
Lord Ashdown, a previously loyal supporter of the Government, joined 25 other Lib Dem peers voting for child benefit to be excluded from the cap calculations.
The former party leader said that as president of the United Nations children's agency Unicef, he was not prepared to back the Government's plans in their current form, denouncing them as "completely unacceptable".
Despite the divisions in his own ranks however, Deputy Prime Minister Nick Clegg has said he is fully signed up to the changes.
Bishop of Ripon and Leeds, the Rt Rev John Packer, who introduced the successful amendment, said: "It cannot be right for the cap to be the same for a childless couple as for a couple with children. Child benefit is the most appropriate way to right this unfairness."
The Government admitted it was "disappointed" by the result but insisted it still intends to push through its plans "in full".
A Department for Work and Pensions spokesman said last night: "We are very disappointed by this decision and it clearly flies in the face of public opinion.
"There has to be a limit on the amount of money benefit claimants can receive.
"We think that limit is set at a fair rate of £26k - the equivalent to someone earning £35,000 before tax, a salary that many working families would be happy to receive.
"If you take child benefit out of the cap it will simply become ineffective, failing the very principle of our reforms, which is to bring fairness back into our welfare system while ensuring that support goes to those who need it.
"We are determined our reforms will be implemented in full and we will take this back to the House of Commons to reverse tonight's decision."
Around 67,000 families will lose £83 a week under the cap, which is due to be brought in from 2013 in England, Scotland and Wales.
Prime Minister David Cameron insisted it was a "basic issue of fairness".
"It's time to call time on these excessive welfare payouts," he added. "That's what the benefit cap will do."
Labour backed the bishops' amendment despite supporting the principle of a benefit cap, insisting it would allow additional safeguards to be put in place when the proposals return to the Commons.
The party's own amendment - exempting those at risk of homelessness from the cap - was defeated by 250 votes to 222.