After winning Tuesday's ballot over changes to a future "meaningful vote" on a final agreement with Brussels in her European Union withdrawal bill, May's plans to end more than 40 years of membership in the bloc were still on track.
Grieve said the problem was that if the United Kingdom reached "the really apocalyptic moment" where no Brexit deal had been done by early February 2019, Parliament was not being offered the chance to say what should happen next - only to "note" the position.
Dominic Grieve, the former attorney-general and who leads the contingent of Tory diehards loyal to the European Union, has said this new version of the amendment is unacceptable and that it takes the "meaning" out of the "meaningful vote" he was demanding.
Mr Grieve told the BBC: "We could collapse the Government, and I can assure you that I wake up at 2am in a cold sweat thinking about the problems that we have put on our shoulders".
On Tuesday MPs in the Commons voted to reject the amendment to the bill, which would weaken the PM's hand at the negotiating table.
The ping-pong process of the withdrawal bill between the two houses of parliament returns to the Lords on Monday, when peers are expected to reject the amendment drafted by May and her team, and insert one modelled more closely on Grieve's idea.
But he branded the amendment finally published by DExEU hours later "unacceptable", because it offered MPs a "meaningless" vote in the case of a no-deal Brexit, allowing them to note the situation but not to determine what should happen next.
India vs Afghanistan, Ist Test, Day 1 - INDIA 347-6 at stumps
The troubled country has yet to play an worldwide game at home and the possibility of doing so in the future is remote as well. This decision of allowing players time to prepare for the Test by monitoring their training schedules was a conscious one.
"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. Other rebels suggested the prime minister had "caved in" to the demands of Brexiteers.
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.
"Grateful for the conversations but without consultation what was agreed earlier today has been changed".
Tory Remainer Sarah Wollaston tweeted: 'So just to be clear we are now going to have to amend the "unamendable" after the agreed amendable amendment acquired a sneaky sting in the tail.
In the House of Commons on Thursday morning, Labor's Brexit spokesman Sir Keir Starmer pressed Brexit Secretary David Davis on seemingly conflicting accounts of what the would-be rebels were offered.
Her concession to discuss the changes may mean lawmakers could have more power if she fails to secure a Brexit deal, possibly leading to a softer approach to Britain's divorce.
She hailed Grieve as a "hero" for supporting a final say on Brexit.
"We need to keep enough control in Parliament to ensure that, if we do Brexit, we do it properly and do not end up with a deal that damages our country for generations to come", he wrote. They can not be trusted with Brexit.