Greening, a former Education secretary who quit May's government in January, is the highest-profile Conservative to support a second vote, though she was not an advocate of leaving the E.U.in the first place.
"There is not going to be a second referendum under any circumstances".
This amendment, as well as many others, will be voted on in the House of Commons today - as Theresa May tries to protect her Brexit plans for the hard-Brexit factions of her own party. "A People's Vote on the final Brexit deal is our chance to tell the politicians just what they think of the deal they have negotiated".
Her Chequers Brexit deal seems to be history only days after the ink on its associated white paper has dried: it is hard to see the European Union agreeing to levy the UK's tariffs, as the ERG amendment demands; and absent that implausible agreement from the European Union, there is no longer a credible customs plan that would keep open the border between Northern Ireland and the Republic (or at least not one that the European Union would recognise).
"It's also quite likely to be either rejected by the European Union or more demands will be made upon it so it will be even less acceptable".
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On Sunday, May attempted to face down would-be eurosceptic rebels by warning that if they sink her premiership then they risk squandering the victory of an European Union exit that they have dreamed about for decades.
Business minister Greg Clark urged party members to get behind the prime minister's plan: "When it comes to parliament I hope and expect that it will be persuasive that what is on offer will be good for the United Kingdom, it would be good for every part of the United Kingdom".
A ministerial aide became the ninth party member to resign their post in protest over the Chequers deal. The debate is due to start at 1430 GMT and end with votes at 2100.
A senior Government source said "no decision yet" had been made on whether to accept the amendments supported by arch-Eurosceptics including Jacob Rees-Mogg, Sir Bernard Jenkin, Priti Patel and Iain Duncan Smith.
But on Brexit, it's clear we have a parliament in stalemate that can't deliver a clear choice for the future.
Former worldwide development secretary Priti Patel, who is proposing one of four amendments to the Taxation (Cross-border Trade) Bill, told BBC Radio 4's Westminster Hour the white paper had "many flaws around our independence and our ability to make free trade agreements". 'We'll have an idea of the numbers, I suppose, at 10 o'clock on Monday evening'.