Church of England bishops and Liberal Democrat peers will join to try to win concessions when the House of Lords votes later on a benefits cap.
Ministers are proposing an annual limit on benefits of £26,000 for households in England, Scotland and Wales.
Opponents claim children, especially from big families, could suffer when the changes come into effect in 2013.
The government believes a cap on benefits would save money and create a fairer welfare system.
But not everyone on the coalition side agrees, so there are suggestions of compromise and concessions.
More detail is expected to emerge soon about “transitional arrangements” that Deputy Prime Minister Nick Clegg has promised to secure to help those affected by the changes.
It has been estimated that about 50,000 families could lose out.
Labour has said it will not vote against the cap but it is likely to propose that vulnerable adults and families with children facing homelessness should not be bound by the change.
Housing Minister Grant Shapps said the system needed to change because it was out of control.
“Benefits have to be fair, not just for the people receiving them,” he said.
“It’s absolutely right we have that safety net for the most vulnerable people. But I think they have to be fair for the rest of the taxpayers who are funding this multi-billion system.
“It can’t be right to say if you are in receipt of benefit you can live above average in terms of the amount of income that you get, more than the average person working.
“So we’re simply saying there should be a benefit cap which is at the average salary.”
While defending the plans, Employment Minister Chris Grayling conceded that some people would be forced to move home because they would receive reduced benefits.
He said they would have to move to an area they could afford.
The former Bishop of Hulme, the Right Reverend Stephen Lowe, told the BBC that capping housing benefit could make children suffer.
He said: “We have got some families, quite a large number of families I am sad to say, where neither parent is working. They perhaps are not particularly capable of working. They have large families.
“At the moment, this policy is making no allowance for them.
“The fact that child benefit, which is meant to be attached to the number of children, is being discounted in relation to this particular £26,000 is actually going to damage those children’s welfare and put potentially another 100,000 children into poverty.”
Former Lib Dem leader Lord Ashdown has said he will vote against the coalition’s plans for a benefits cap.
The peer said he could not back the proposal without measures to cushion the impact on those affected.
Work and Pensions Secretary Iain Duncan Smith has urged those opposed to aspects of the cap, including leading bishops, to think about those who pay taxes while some unemployed people live in large houses at public expense.
Mr Duncan Smith admitted his plans for a cap on working-age benefits of £500 a week or £26,000 a year – equivalent to the average wage earned by working households after tax – could face defeat in the Lords on Monday.
He told BBC Breakfast: “We have a year before this comes in. We now know exactly which families [the cap will affect] what their size is, where they live.
“It’s not about punishing them, it’s about saying – look, if you live in a house that you couldn’t afford if you were in work, then you’re disincentivised from taking work.
“We want people to find work, we want them to be in work.”
Mr Duncan Smith also said that the public is “overwhelmingly in favour” of the cap, adding that “even Labour and Liberal voters are overwhelmingly in favour of fairness to the taxpayer as well as fairness to the benefit recipient”.
Peers have already inflicted a series of defeats on the government’s flagship Welfare Reform Bill but ministers say they are determined to get key changes through Parliament.
The changes would affect England, Wales and Scotland. Northern Ireland has its own social security legislation, but it is expected that what is approved at Westminster will likely be introduced there as well.
A small number of provisions will apply directly to Northern Ireland, regarding the abolition of benefits, state pension credit, tax fraud investigation and information sharing about tax fraud.