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.
"We could collapse the government, and I can assure you I wake up at 2 a.m.in a cold sweat thinking about the problems we have put on our shoulders", Dominic Grieve, a leading pro-EU lawmaker negotiating with the government, told the BBC.
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.
Yet Brexiteers, including Jacob Rees-Mogg put pressure on the Government not to agree to the main thrust of the Remainers argument that Parliament should be able to instruct the Government how to negotiate with Brussels.
However, the amendment to the EU Withdrawal Bill tabled yesterday leaves Parliament facing a "deal or no deal" choice.
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.
Asked what he would do next, on BBC One's Question Time, he said: "I think a group of us will talk further to the government and try to resolve it".
Mr Grieve had originally wanted the amendment to say that the government must seek the approval of Parliament for its course of action - and that ministers must be directed by MPs and peers.
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French coach Didier Deschamps said: "It was a highly hard match, it was complicated, the Australian team was very good". The Socceroos can take enormous encouragement after they more than held their own against the Euro2016 finalists.
Instead, the majority of the pro-EU Tories backed the Government in voting down a Lords amendment to give them the power to tell ministers to go back to Brussels and renegotiate.
The Prime Minister has insisted she did not break her word on Parliament having a meaningful vote on final decisions about Brexit, but argued that MPs can not expect to "tie the hands of Government in negotiations".
"It all changed without Dominic Grieve or anyone else being consulted".
On Wednesday, the amendments will return again to the Commons, where May faces the possibility of defeat over a meaningful vote.
May is struggling to unite the Conservative Party around her plan for leaving the European Union, trying to balance the demands of those who want the closest possible ties with the bloc and others who want a clean break.
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.
Shadow Brexit secretary Sir Keir Starmer said: "The Government's amendment is simply not good enough".
Pro-EU lawmakers, however, welcomed it as a signal that the government was moving towards ruling out a hardline "no deal" Brexit.
"The people must be given the final say on the deal, and an opportunity to Exit from Brexit".
Mr Tugendhat suggested there was no need to "beef up" the "meaningful vote" which now offers parliament the choice between the government's deal and Britain leaving the European Union with no deal.