Under these circumstances, a minister must make a statement in Parliament within 14 days and give MPs an opportunity to vote.
Tensions heightened after former attorney general Dominic Grieve warned that the Tory rebels he leads could "collapse" the Government if they disagree with the final outcome of withdrawal talks, and had the right to a proper say on Brexit.
Crucially, the motion will be unamendable, meaning that MPs can not insert a requirement for May to go back to the negotiating table, extend the Brexit transition or revoke the UK's withdrawal under Article 50.
"Parliament can't tie government's hands in negotiations".
"My intention is to support Dominic Grieve in the amendment that he put before the house, because that's what I publicly stated last Tuesday", he told Sky's Sophie Ridge on Sunday show.
Using words like "bad faith" and "betrayal", pro-Remain Tory MPs have accused the Government of ripping up an agreement they had made with Theresa May earlier this week.
Now Conservative peer Viscount Hailsham has re-tabled Mr Grieve's amendment in the House of Lords, setting the scene for a fresh Government defeat when the Bill returns to the Second Chamber on Monday.
Davis and Prime Minister Theresa May have argued that they can not accept anything which gives parliament the power to bind their hands in negotiations with the European Union, or opens the door to lawmakers overturning the result of the 2016 Brexit referendum.
That was the frank message from Tory MP Mike Wood, who has warned his fellow politicians that people are sick and exhausted of them bickering amongst themselves over the UK's departure from the EU.More news: Second deputy dies in shooting in Kansas
The Prime Minister is facing the biggest parliamentary bust-up yet on her flagship Brexit legislation after a compromise created to keep critics in her own party on board was denounced as "unacceptable" by Tory Remainers.
Speaking on why she voted against the government, Soubry tweeted "I voted in favour of the Lords amendment because I feared she would not be able to deliver on her promise because she won't see off the no deal hard Brexiteers". "Grateful for the conversations but without consultation what was agreed earlier today has been changed".
House of Lords rejected on Monday Prime Minister Theresa May's plan to give MPs a so-called meaningful vote on her Brexit strategy, instead backing a rival proposal that gives parliament more influence.
"Would be amusing if only it wasn't such a serious issue, Preventing the most destructive Brexit matters to the majority in Parliament..."
Mr Wood was reflecting on a tumultuous week of votes in the House of Commons, which saw Labour and Tory MPs rebel against their parties on key legislation.
Shadow Brexit secretary Sir Keir Starmer said: "The Government's amendment is simply not good enough".
Leading pro-EU Conservative Dominic Grieve said the compromise "cannot be accepted".
He told the BBC: "I can't save the Government from getting into a situation where Parliament might disagree with it".