The key vote which has taken place is whether MPs will have a "meaningful vote" - amendment 19 proposed by the Lords - on the final Brexit agreement.
After months of debating the detail of the legislation that will trigger United Kingdom withdrawal from the European Union, the House of Commons will stage crucial votes on Tuesday and Wednesday that will decide her fate.
"In all conscience, I can not support the Government's decision to oppose this amendment because doing so breaches such fundamental principles of human rights and Parliamentary sovereignty".
But the resignation by Phillip Lee, who has always been critical of the government's Brexit strategy, underlined the deep rifts in the party over Brexit that makes such votes anything but easy.
Members of Parliament decided by 324 votes to 298 - a majority of 26 - to reject a House of Lords amendment to the EU Withdrawal Bill.
After winning Tuesday's vote on changes to a future "meaningful vote" on a final agreement with Brussels in her European Union withdrawal bill, May's plans to end more than 40 years of membership in the bloc were still on track.
The Government has won this key vote, but not without having to make some significant concessions.
The concession on a meaningful vote came after intensive horse-trading on the floor of the House of Commons, with chief whip Julian Smith shuttling between Tory backbenchers during debate on Lords amendments to the EU Withdrawal Bill.
Asked on BBC Radio 4's Today programme what would happen under Government plans if MPs voted against the deal eventually secured by Mrs May, Mr Davis said: "If they throw it out, well, they throw it out".
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Kim, for his part, said the leaders had "decided to leave the past behind" and promised: "The world will see a major change". Trump said he urged Kim and other North Korean officials to watch a four-minute video produced before the Singapore summit.
Phillip Lee, who resigned this morning, gave an impassioned speech from the "naughty corner" on the backbenches - flanked by Remainers including Bob Neill, Nicky Morgan, receiving congratulations for his decision by Soubry and Sarah Wollaston.
It is thought that both the government and the Remainer group of Tory MPs consider the outcome to be a success.
He confirmed that ministers will seek to overturn 14 amendments which he said would undermine the goal of the Bill and fail to respect the result of the 2016 referendum.
She said unless there was a "meaningful vote" Parliament would be left with "the grim choice between a poor deal and exit with no deal at all".
Meanwhile, Tory Brexiteer Bernard Jenkin told the government he would not accept ministers agreeing to Mr Grieve's demand for the House of Commons to assume control of Brexit negotiations in the event of no deal.
That effectively rules out threatening the European Union with a no-deal Brexit, because the Commons will not approve a no-deal Brexit.
His resignation came hours before British Prime Minister Theresa May faces crunch votes in parliament and a potential showdown with pro-EU rebels in her ruling party over whether parliament can prevent a no-deal Brexit.
Overall MPs voted against the House of Lords' amendments in three separate votes.
"We will wait and see the details of this concession and will hold ministers to account to ensure it lives up to the promises they have made to Parliament".