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).
The contest was prompted by ex-prime minister David Cameron's decision to quit the House of Commons after departing 10 Downing Street in the wake of the Brexit vote.
She added: "Things have moved on from that very clear message that Brexit means Brexit, and that is why we are rightfully questioning the legislation, putting forward new clauses and amendments, and saying not just to the Prime Minister but the whole of government reconsider, look again and work with us".
Another pro-EU Conservative lawmaker Dominic Grieve, who has led previous efforts to get the government to soften its Brexit stance, said the party needed to accept compromises "or accept that Brexit can not be implemented and think again about what we are doing".
His resignation follows that of foreign secretary Boris Johnson and Brexit secretary David Davis, as dissatisfaction with Theresa May's Brexit deal proposed at Chequers spreads throughout the government.
"Many people voted from the heart to leave the European Union", she said.
She asked: "Who is in charge?.is it the prime minister or is it the member for North East Somerset [Jacob Rees-Mogg]".
"I'm sure Theresa May does not want to split the Conservative Party and therefore she will find that the inevitable outcome of the parliamentary arithmetic is that she will need to change it (the Brexit policy) to keep the party united", Rees-Mogg said.More news: Caribbean American legislator arrested for protesting Trump Supreme Court nominee
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A Labour source told HuffPost: "Theresa May sounds like she is running scared of her own MPs".
Mr Johnson also made his first public intervention since his resignation last week, with a column in the Daily Telegraph pledging to resist "for now" the urge to "bang on about Brexit".
The report stage of the bill will also see MPs debate a long-awaited amendment that would keep the United Kingdom in the EU customs union post-Brexit that is supported by Labour, the SNP, the Lib Dems and two Tory Remainers, Anna Soubry and Ken Clarke.
May spent the weekend defending her plan, and did so again in a speech at Farnborough airshow Monday, insisting it would protect trade in goods with the European Union and avoid border checks in Ireland. She said she and other senior Conservative Party lawmakers favour a new vote.
"We need to keep our eyes on the prize".
Conservative former Cabinet minister Ken Clarke told MPs that the Government's adoption of ERG amendments was "directly inconsistent with the white paper of a week ago".
He described Ms Greening's call for a second referendum as "a little ill-thought out", saying: "If we wanted to extend the uncertainty for another long period this is one way of doing it".