The opposition Labour Party wants to force the government to negotiate a Brexit deal where the United Kingdom retains "full access" to the EU's single market and that would ensure "no new impediments" to trade.
These were the words of a minister expecting to win the vote.
Dr Lee's shock departure came as Brexit Secretary David Davis warned potential Tory rebels that they can not undo the European Union referendum, ahead of a tricky 48 hours in which the Government will try to get its Brexit programme back on track.
During a frantic day of discussions between ministers and Conservative backbenchers, potential rebels were eventually persuaded to back down when Solicitor General Robert Buckland told MPs that ministers were willing to "engage positively" with their concerns.
Ministers had initially refused to even consider Grieve's amendment but moved to accept it at least in part, after whips signaled that the government were likely to lose in the Commons.
However, despite backing down, pro-Remain Tories signalled they would not be easily consoled by a compromise offered by ministers.
In his resignation letter, he said he wouldn't be able to "look my children in the eye" if he supported Brexit in its "irresponsible" current form.
Details of the government's commitment will have to be formalised next week in a new amendment to the bill.
She won a succession of votes on Tuesday overturning Lords amendments, including one which would have removed the date of Brexit on March 29 2019 from the text of the Bill.
MPs would then be permitted to vote on the final Brexit deal, igniting fear in Brexiteer MPs, as parliament could also halt the Brexit process entirely.
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"This justifies my decision to resign and makes it a lot less painful".
During Tuesday's debate, Ms Soubry told the House of Commons that a fellow Remainer MP had to be guarded by six armed undercover police officers at a recent public event.
Well what the Remainer MPs thought they heard from May does not seem compatible with Davis's red lines.
Soubry reminded the House of Commons of the 48% who were being ignored by the government.
'They want us to deliver on Brexit and build a brighter future for Britain as we take back control of our money, our laws and our borders'.
Asked whether such concessions would nowAsked whether such concessions would hamper Britain's negotiating hand, Mr Grieve continued: "I disagree with that entirely".
Despite depending on the votes of the 10 DUP MPs for her precarious Commons majority, there were signs of cautious optimism among ministers that they would get the numbers to see off the revolt.
Despite many Conservative MPs who backed Remain in the referendum, just two rebelled against the government on a meaningful vote.
Following the vote, shadow Brexit secretary Sir Keir Starmer said: "Facing the prospect of a humiliating defeat Theresa May has been forced to enter negotiations with her backbenchers and offer a so-called concession".