Attention has focused on June 12 on the so-called "meaningful vote" amendment, which would give parliament the power to decide what to do if it rejects the final Brexit deal.
The amendment in question hinges on whether lawmakers will get a "meaningful" vote on Britain's membership of the European Union.
The pro-European cause was boosted when junior justice minister Phillip Lee, a close personal friend of the prime minister, resigned shortly before the debate in order to back the veto amendment.
As with last week's set-to with Davis over the Northern Irish backstop, both sides of the Brexit culture war in the Tory party were nearly immediately in dispute about what the climbdown meant - and who had won. The strength of this commitment is yet to be seen in writing - and the Brexit department is still insisting it has not given up control of the negotiations - but the anti-Brexit rebels showed they have the numbers to force a defeat should the government renege on its pledge.
"If Brexit is worth doing, then it is certainly worth doing well; regardless of how long that takes", he said. Brexit-backers objected as it would have all but removed the no-deal nuclear option from negotiators' arsenal.
'The objective of the EU Withdrawal Bill is simple - it is putting EU legislation into law to ensure a smooth and orderly transition as we leave, ' she is expected to tell them.
There is a gap between what the Tory Remainer rebels think the prime minister promised them and what the Brexit Secretary David Davis thinks has been promised.
Lee's resignation came as May's fragile minority government scrambled to shore up support among lawmakers before two days of debate and votes in the House of Commons on its flagship Brexit bill.
He confirmed that ministers will seek to overturn 14 amendments which he said would undermine the objective of the Bill and fail to respect the result of the 2016 referendum.
The right-wing press is presenting the upcoming votes as a make-or-break moment, continuing its longstanding tactic of describing the Brexit process as the "will of the people" and any attempts to seek greater democratic oversight of the process as "undemocratic".
In a major climbdown, they said that ministers would consider key aspects of the controversial amendment by Mr Grieve.
"Grieve's amendment puts that right and in a way Govt could and should accept it".
In a concession, the government promised that lawmakers would have a say on what to do next if there is no agreement with the European Union, or if Parliament rejects the deal offered.
It would also give hard Brexiteers the chance to "scupper a good deal", she claimed.
Addressing Conservative backbenchers in Westminster on Monday evening, the Prime Minister warned if a series of Lords amendments to the EU Withdrawal Bill are approved by MPs, it will send the wrong message to Brussels.
However, the compromise is only likely to delay a full-blown showdown on the customs union until trade legislation returns to the Commons in July.