The government's amendment to the EU Withdrawal Bill sets out what must happen if the prime minister announces - before 21 January 2019 - that no deal has been reached with the EU either on the withdrawal agreement or the future relationship.
Prime Minister Theresa May's Brexit plans face rejection by parliament's upper chamber on Monday, setting the stage for a confrontation with rebel lawmakers later in the week which could rock her minority government.
The chances of the government being defeated when the Bill returns to the House of Commons later this month has now risen significantly, with trust between May and her MPs at an all-time low.
Davis and 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.
Speaking to Channel 4 News, Soubry said: "This amendment has changed so everything that said we would get that meaningful vote - it is now completely meaningless". He added he would listen to the government but "I hope they listen to me when I say I don't understand why you've done this last-minute switch".
Ministers have so far agreed to give parliament a symbolic vote on the government's strategy if its initial exit deal is rejected, but not to give parliament the power to force changes to its plan. The spokeswoman said the government had listened to MPs who had called for the "ability to express their views, in the unlikely event that our preferred scenario did not come to pass".
Griezmann announces decision about his future
I can't take it anymore, I need to tell the people that I want to stay", he said. He has cooled me because it was very hot". "It's incredible.
The rebels, led by former minister Grieve, stepped back from defeating the government on Tuesday after they were privately told that a concession on a no-deal veto would be forthcoming.
This trend toward a soft Brexit has alarmed euroskeptic campaigners including Foreign Secretary Boris Johnson, who fears the United Kingdom could end up forever in the EU's orbit, rather than breaking free to strike trade deals with other countries around the world.
He told BBC One's Sunday Politics: "And I can assure you I wake up at 2am in a cold sweat thinking about the problems that we have put on our shoulders".
"This amendment I guess may be amended and if that is acceptable I will support that but fundamentally I resigned to support parliament getting a proper truly meaningful vote on the deal to leave the European Union".
"As Parliament gradually assumes a bigger role in the process, the debates have made a "no deal" exit next March less likely and a softer Brexit more likely", Mujtaba Rahman, managing director at Eurasia Group, said in a note.
"The Government's amendment is simply not good enough", the Shadow Brexit Secretary Keir Starmer said. Instead, MPs will be offered a vote on an unamendable statement, which would effectively turn any vote into to a vote of confidence in the prime minister.