Tory former chancellor Lord Lawson has joined calls for George Osborne to "tweak" cuts to tax credits to protect poorer households.
But the peer hit out at "wholly wrong" attempts to kill off the policy altogether in the House of Lords.
The Chancellor is under mounting pressure from within Conservative ranks to find ways to limit the impact of the move on low earners.
Senior backbenchers are threatening to rebel in a Commons vote next week in a bid to force his hand.
Lord Lawson told BBC Radio 4's Today programme that reducing the tax credit bill was "absolutely right" but there "may be areas where there could be some tweaking.
"You cannot remove these tax credits without people being worse off. The question is who is going to be worse off," he said.
"People are going to get better off as the economy grows, and it is growing and we want a successful economic policy to ensure it continues to.
"But there is a problem.
"Tax credits go a long way up the scale. It goes up to half the families in the land. And so the tweaking would be to make the burden - and there is always a burden when you make these tough decisions to cut tax credits - rather less for the people towards the bottom end of the scale."
The independent Institute for Fiscal Studies calculates that the higher national minimum wage promised as part of the reforms would not compensate entirely for the loss of tax credits.
Liberal Democrats have tabled a so-called "fatal motion" in the House of Lords which would axe the £4.4 billion cut altogether if approved on Monday.
Labour and crossbench peers are also pushing votes that would refuse to sign off on the policy until the Government had considered changes.
Prime Minister David Cameron has warned the upper chamber not to defy convention that it does not block financial measures.
Lord Lawson said: "It is a matter for George Osborne, on reflection, to look at and make changes if he feels necessary in his Budget in the spring.
"It would be wholly wrong constitutionally, wholly wrong, for the unelected House of Lords - which should debate it and argue about it - to do anything that would kill something of a financial nature which has been through the House of Commons, approved by the House of Commons not once but twice."
That principle "was supposed to have been settled" by the 1911 Parliament Act, he said.
"It is of the first importance, constitutionally, that the House of Lords does not try and arrogate to itself the right, on a financial matter, to overturn in any way something which has passed through the House of Commons not once but twice."