If they agree once again that "sufficient progress" on key issues like the Northern Ireland border, the rights of their citizens living in Britain - and the so-called "divorce bill" - it would be a huge blow to Theresa May's chances of getting a deal done before the end of Article 50.
The lobbying group last month said it was "extremely concerned" with the slow pace of Brexit talks and called on the Government to come up with measures to speed it up.
The move was seen as an attempted concession to Tory rebels ahead of votes this week on the separate EU (Withdrawal) Bill, also known as the repeal bill, with the Government facing potential defeat on plans to guarantee MPs a "meaningful vote" on the deal.
Mr Davis said that the new law will enable Parliament to go through the legislation on a "line-by-line" basis, but raises the prospect of a divisive parliamentary showdown on the eve of Brexit.
Tellingly, it comes as the government try to persuade Tory rebels to play ball over the EU Withdrawal Bill which returns to the House tomorrow - and this concession is aimed directly at an amendment to that nature from Dominic Grieve.
"It is clear that we need to take further steps to provide clarity and certainty both in the negotiations and at home regarding the implementation of any agreement into United Kingdom law", said Davis, outlining the plans for legislation.
MPs will now be asked to consider a Withdrawal Agreement [and Implementation] Bill.
Some MPs welcomed the move, but others said the change in procedure would mean that if Britain failed to negotiate a deal with the European Union, parliament would have no say, and that there would not be time for a proper chance to have sway over a deal.
However, the offer was immediately attacked by both Labour and Conservative politicians, who expressed anger that it did not give parliament any say in the case of a no-deal Brexit.
"It's a transparent and fairly desperate attempt at the eleventh hour to save face and avoid losing votes in the House".
Before Remainers get the prosecco out, it's worth noting that Davis said in the event of a "no deal" scenario, MPs and peers would not have any vote as there would not be anything to have a bill based on.
"Ministers need to do much better".
British MP's are preparing to vote on the final Brexit bill, which will be implemented by March 2019. They include Dominic Grieve, the Conservative former Attorney General, who previously tabled an amendment to the European Union withdrawal bill demanding a vote.
Moreover, he said that MPs would also have the opportunity of amending the final piece of legislation, after it is presented to parliament.
The Cabinet minister added it was down to political will and he was "quite certain the political will is there".