Chancellor George Osborne will listen carefully to concerns over cuts to tax credits if peers back down over plans to block the move, the House of Lords has been told ahead of a series of crucial votes.
The Government is facing intense opposition to its controversial welfare reforms, which will slash £4.4 billion from working tax credit and child tax credit for some of the country's poorest households.
Ministers are urging critics in the Lords to express their anxiety by backing a motion tabled by Church of England bishops expressing "regret" over the impact while allowing the cuts to complete their parliamentary passage.
But Labour believes sufficient crossbench peers can be persuaded to back its bid to delay the cuts until the Treasury consults further and promises "full transitional protection" for at least three years.
A rare "fatal motion" tabled by Liberal Democrats that would kill off the changes has not won Labour backing so is unlikely to succeed.
Ministers have warned peers against challenging the primacy of the elected House of Commons, which has voted three times on the issue.
Lords Leader Baroness Stowell of Beeston told peers she had talked to Mr Osborne ahead of the debate.
"He would listen very carefully were the House to express its concern in the way that it is precedented for us to do so by the Bishop's amendment," she said.
More than three million families will lose an average of £1,300 a year from April but the Government said eight out of 10 would be "better off" overall from a package which also includes increases in the minimum wage for over-25s, rises in the income tax threshold and extended free childcare.
The respected Institute for Fiscal Studies (IFS) says higher wages will make up for only a fraction of the loss of income - and the Chancellor has refused to publish Treasury analysis.
Ministers are urging the Lords to respect century-old conventions that the unelected upper chamber does not block financial measures approved by the Commons or manifesto commitments.
Senior figures have warned of serious repercussions, with Prime Minister David Cameron even failing to rule out handing out a hundred of more new Tory peerages to give his party a majority.
But peers insist they are free to act because the measures were not specifically set out before May's election and are being pushed through as a Statutory Instrument (SI), not a formal Bill. Asked in a pre-election TV debate whether he planned to cut child tax credit, David Cameron replied: "No, I don't want to do that."
The Prime Minister's official spokeswoman said: "The policy is the policy. It has been voted in favour of three times in the Commons.
"There is a long-standing convention that the House of Lords respects the House of Commons's view on financial matters.
"The Government was elected on a mandate to reduce the welfare bill to make savings of £12 billion. This is part of it. It is about choice. The Government has set out changes here to tax credit that allows you to do more measures to encourage people to work."