Theresa May has suffered a ministerial resignation ahead of crunch Commons votes on Brexit.
Remain-supporting Phillip Lee quit as justice minister, saying "if Brexit is worth doing, then it is certainly worth doing well" and it is "irresponsible to proceed as we are".
He said his main objection to Government policy was over the "wish to limit Parliament's role in contributing to the final outcome" - the so-called meaningful vote amendment.
His shock departure came as David Davis warned potential Tory rebels that they cannot undo the EU referendum, ahead of a tricky 48 hours in which the Government will try to get its Brexit programme back on track.
The Brexit Secretary spoke after some Conservatives signalled that they would support an amendment to the EU (Withdrawal Bill) tabled late on Monday by former attorney general Dominic Grieve giving more power to MPs.
The Commons begins two days of debate and votes on the Bill on Tuesday and Mr Grieve's amendment calls for a binding motion to be passed by the Commons, setting out how to proceed in the event of a "no deal" Brexit.
But Mr Davis told BBC Radio 4's Today programme: "A meaningful vote is not the ability to reverse the decision of the referendum.
"We will put in front of Parliament the decision for them to vote ... after that there will be a process of primary legislation to put the actual details of it in Parliament, so Parliament will actually decide on the application of the detail."
Asked what would happen if they voted against the deal, he said: "If they throw it out, well, they throw it out. We will have to go away, think about it and come back and make a statement, which is what I am saying to the House this afternoon."
The Prime Minister appeared to have defused a potentially explosive row over the EU customs union on Monday night as Tory pro-Europe rebels Sir Oliver Letwin and Nicky Morgan and Brexiteers Jacob Rees-Mogg and Sir Bill Cash came together to table a separate compromise amendment backing "a customs arrangement" with the EU.
Government sources signalled to the Press Association that ministers were set to back the move. However, the compromise is only likely to delay a full-blown showdown on the customs union until trade legislation returns to the Commons in July.
Mrs May set the tone for a tense two days as she warned Tory Remainers that if they defied her and backed Lords amendments to the landmark Brexit legislation it would weaken Britain's hand at the negotiating table.
Addressing a meeting of the backbench 1922 Committee on Monday, ahead of the key votes, she said: "I am confident I can get a deal that allows us to strike our own trade deals while having a border with the EU which is as frictionless as possible.
"But if the Lords amendments are allowed to stand, that negotiating position will be undermined."
However, Devon Tory Sarah Wollaston signalled on Tuesday morning that she would back Mr Grieve's amendment.
Dismissing the Government's compromise, she tweeted: "Merely issuing a statement in response would make it a meaningless final vote.
"Grieve's amendment puts that right and in a way Govt could and should accept it."
She said unless there was a "meaningful vote" Parliament would be left with "the grim choice between a poor deal and exit with no deal at all".
It would also give hard Brexiteers the chance to "scupper a good deal", she claimed.
Sir Oliver defended his compromise agreement, saying it was "sensible" in delaying a vote on the customs plan until details were more settled.
Asked on Today if the amendment "just kicked the can down the road", he replied: "That is a very sensible thing to do.
"If you are engaged in trying to sort something which is complicated out, it makes sense to do it when you know what the thing that you are debating looks like."
Meanwhile, Ireland's premier raised the possibility of delaying Brexit to allow more time to negotiate the UK's exit deal.
Taoiseach Leo Varadkar said extending the March 29 2019 departure date was one of a number of "different scenarios" that could be pursued if a withdrawal agreement fails to materialise in the coming months.