Downing Street has rejected Justine Greening's call for a fresh referendum on the UK's exit from the EU, saying it will not happen "in any circumstances".
The former education secretary argued the final Brexit decision should be given back to the people and out of the hands of "deadlocked politicians".
She called for three options to be on the ballot paper: the prime minister's Chequers deal, staying in the EU or a clean break from Europe with no deal.
The UK is due to leave in March 2019.
Amid continuing Tory divisions over Mrs May's strategy, the government has accepted changes to legislation for customs arrangements after the UK leaves to avoid a Commons rebellion by Brexit-backing MPs.
No 10 said the amendments to the Customs Bill, including one that would preclude the UK from collecting tariffs on goods bound for EU countries, were "consistent" with the blueprint agreed by the cabinet.
Asked during a Commons statement on last week's Nato summit whether she was "rolling over", Mrs May said she would continue to "listen to the concerns" of colleagues regarding Brexit-related legislation.
Ms Greening, who resigned after the cabinet reshuffle in January, said the referendum should offer a first and second preference vote so that a consensus can be reached.
Speaking on BBC Radio 4's Today programme, Ms Greening said the government's proposals were a "genuine clever attempt at a compromise that could work" but "suits no-one".
The MP for Putney said: "The reality is Parliament is now stalemated. Whatever the proposal on the table, there will be MPs who vote it down. But Britain needs to find a route forward."
Ms Greening, who supported Remain in the EU referendum, is the highest profile ex-Cabinet minister to call for a second referendum.
She said there were other senior Conservatives who agreed with her stance, adding that people who supported Leave in the referendum would also feel the government's approach is "not what they voted for".
In her article in the Times, she lambasted the PM's Brexit blueprint, saying: "We'll be dragging Remain voters out of the EU for a deal that means still complying with many EU rules, but now with no say on shaping them.
"It's not what they want, and on top of that when they hear that Leave voters are unhappy, they ask, 'What's the point?'
"For Leavers, this deal simply does not deliver the proper break from the European Union that they wanted."
'Another one joins the gang'
By Chris Mason, BBC political correspondent
Combine a hung parliament with Brexit, and when you scan your eye around the House of Commons, you sometimes wonder if they can collectively agree on anything.
The one thing there is certainly not much public support for right now among MPs is another referendum.
Whatever the view of an individual MP on Brexit, most see making the case for another schlep to the polling station a hard argument to flog.
And so while those doing so are a pretty small tribe, and it is a million miles from a majority view, there is pride among them that they can add another name to their gang.
But it is worth remembering that Justine Greening is a pro-European in a marginal seat - Putney in London - that voted heavily to Remain.
Ms Greening, who grew up in Rotherham, where 68% people voted to leave the EU, said the parliamentary stalemate "risks a no-confidence vote and, worse, a Corbyn government, which would be disastrous for the economy".
She had previously suggested a future generation of MPs will seek to "improve or undo" Brexit if it does not work for young people.
Fellow Tory MP Sir Bernard Jenkin, who backed Leave in the referendum, said he agreed with Ms Greening that the PM's plan was "dead" but described her call for a second vote as "a little ill-thought-out".
"If we wanted to extend the uncertainty for another long period this is one way of doing it," he told Today.
Mrs May has ruled out a second vote, as has Labour leader Jeremy Corbyn, although a number of senior Labour figures are backing the cross-party People's Vote campaign for a final vote on any exit deal.
Pro-EU Conservative MP Dominic Grieve told BBC Radio 4's The World at One programme the possibility of holding a second referendum should not be excluded but Mrs May was "entitled to try to develop" her Chequers plan.
"My primary political duty at the moment is to try and help get this country through a Brexit process that is endangering its stability and its wellbeing," he said.
Former UKIP leader Nigel Farage said another referendum was "heading much closer" but could be avoided if the Tories changed leader, adding there was "uproar out there" about the prime minister's proposals.
Suella Braverman, who used to lead a Eurosceptic group of Tory MPs and is now a minister in the Brexit department, said there were "obviously strong views" within her party and described the Chequers plan as a "starting point" for negotiations with the EU.
But the disagreements in the party have also led to another resignation from the government.
Scott Mann has quit his job as a parliamentary private secretary at the Treasury, saying Mrs May's plan was "in direct conflict" with the views of his Leave-voting constituents in north Cornwall and he did not want to deliver a "watered-down Brexit" to them.