Mrs May avoided nearly certain defeat in the House of Commons on Tuesday by inviting potential rebels into her private office and assuring them that their concerns about having a "meaningful vote" on the final Brexit deal would be addressed.
Instead, MPs would be allowed to vote only on a "neutral" motion, confirming that they have considered a statement by a minister on the issue.
He said: "I think it is unacceptable because it seems to me to be contrary to what the whole intention was behind this whole amendment".
Despite the "vitriol" directed towards the rebels, "there is not a single MP who does not agree that getting the [withdrawal] bill on the statute book is essential for us all".
However, the Grieve amendment was not put to a vote on Tuesday, after would-be rebels accepted "personal assurances" from the PM that a compromise would be found.
Asked if voting against the Government could bring it down, Mr Grieve told BBC1's Sunday Politics: "We could collapse the Government".
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Under the Government's plan, MPs will only be able to debate the Prime Minister's next move if no deal is struck or they vote down the deal, and would have no power to direct what should happen next.
The rebels are seeking both closer ties with the European Union on issues like trade and customs, and to ensure that the government does not follow through on its threat to leave the bloc without a deal if it does not like the terms on offer from Brussels.
The dispute between the government and a group of soft Brexit Tories centers around a "meaningful vote" on any eventual deal negotiated with Brussels, created to enable MPs to vote down the final agreement without risking leaving the European Union with no deal at all.
Pro-EU Tories were quick to voice their anger.
The minister leading those negotiations, Solicitor General Robert Buckland, said the ruling minority Conservative government was standing by its own proposal, rejected by party rebels last week.
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Sarah Wollaston, who is also unhappy with the current state of the government's flagship Brexit bill, claimed a compromise agreed with ministers had "acquired a sneaky sting in the tail" by the time it was formally tabled.
He said: "Theresa May has gone back on her word and offered an amendment that takes the meaning out of the meaningful vote".
In the final text of the amendment published on Thursday, no effective veto on a no-deal Brexit is offered to MPs. "Parliament can not - and should not - accept it".
"The people must be given the final say on the deal, and an opportunity to Exit from Brexit".
"The Government's position has not moved since last year's white paper, and even Labour's manifesto was quite clear that free movement of people is not consistent with Brexit, and that we must have the freedom to conclude global trade deals".
Brexit minister David Davis had earlier warned lawmakers that the government would never allow them to "reverse Brexit" or undermine negotiations.
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The vote was really about "who controls the Brexit deal that the government hasn't negotiated yet".