The Chancellor is "in listening mode" over mounting Tory demands for action to soften the impact of tax credit cuts on low-income households, cabinet colleague Nicky Morgan suggested.
The Education Secretary hinted that George Osborne could use his Autumn Statement to announce further measures to offset the £4.4 billion a year welfare squeeze as the Government faced a showdown with the House of Lords.
Peers will vote tomorrow on moves to throw out the reform package or block it until ministers find ways to prevent poorer working families suffering a sudden £1,300 average loss of income from April.
Ms Morgan insisted there was no question of the cuts being dropped - after shadow chancellor John McDonnell said Labour would refrain from exploiting any U-turn for party political advantage.
She urged the House of Lords not to provoke a potential constitutional crisis by striking down a finance measure already backed by MPs, despite Tory critics defending the right of the upper chamber to force a re-think.
But asked if Mr Osborne could meet calls for mitigating measures, she told BBC1's Andrew Marr Show: "The Chancellor's track record has very much been about supporting, in budgets, working families.
"He very much is always in listening mode."
She added: "Not the main policy, the Prime Minister has been very clear that the policy is not going to change."
Liberal Democrats have tabled a rare "fatal" motion that would force the Government to resubmit its policy to Parliament, while a Labour amendment instead seeks a fresh consultation and "full transitional protection for a minimum of three years".
Ministers are urging critics instead to back a motion tabled by Church of England bishops that would express "regret" at the failure to consider the impact but allow the cuts go complete their parliamentary passage.
Mr Osborne insisted this week he was "comfortable" with the policy despite analysis by the independent Institute for Fiscal Studies (IFS) that the introduction of a higher minimum wage will not offset poor households' losses.
Ms Morgan conceded people would be concerned when they received letters in the run-up to Christmas setting out the cuts in their payments but accused opponents of failing to take into account the "broad package" of economic boosts.
"People are of course going to be worried ... but I think it's a question of working through all the numbers. But what is the alternative? We have to get the economy straight."
Mr McDonnell said that if people were "properly protected" from the present plans then "at the right time, if there is a way of reducing tax credits, of course we will cooperate with them".
"It can't be a fudge. Not some partial reversal that scores cheap headlines, yet leaves people still worse off or lands another burden on middle and low earners or the poorest in our society," he told the Chancellor in a letter.
"I am appealing to you to put the interests of these three million families ahead of any concerns you may have about losing face and ahead of petty party politics."
Joking about the flak he took for changing his mind over support for the Government's fiscal charter, he wrote: "I promise you personally and publicly that if you U-turn and reverse this decision fairly and in full, I will not attack you for it."
Ruth Davidson, the leader of the Scottish Tories, became the latest senior figure to demand a rethink, warning the present policy would cause unacceptable "suffering" for poorer families.
"The aim is sound, but we can't have people suffering on the way," she told the Mail on Sunday.
"The idea that there's a cliff edge in April before the uptake in wages comes in is a real practical human problem."
Senior backbencher David Davis and London mayoral candidate Zac Goldsmith have joined forces with Labour's former welfare minister Frank Field on a cross-party motion calling for action to protect poorer families.
It will be put to a non-binding vote in the Commons on Thursday.
Mr Davis backed the right of peers to demand a re-think - though stopped short of backing the "fatal" motion - arguing it was only possible because MPs had been denied sufficient chance to amend the proposals.
"Had the Commons been given a proper chance to think in the first place this circumstance would never have arisen," he said of the decision to push it through via statutory instrument, not the Finance Bill
"Let us recognise that it was a mistake, remember that the strongest stance is often the one of most flexibility, and thoughtfully and carefully put it right," he wrote on the CapX website.
Tory former cabinet minister Lord Heseltine said fellow peers were "playing with fire" by threatening to block the reforms.
"The Commons are going to win this issue one way or another but the most likely losers are the House of Lords themselves who will find their powers curtailed or stripped or whatever it may be," he told Sky News.
Ex Conservative leader Lord Howard said there were "quite likely to be consequences" and Tory Jacob Rees-Mogg said it would be "perfectly proper" to flood the upper chamber with new Tory peers to ensure a Government majority.
But Mr Davis dismissed that prospect which he said would be seen as "one of the biggest acts of constitutional vandalism in modern times".