The government tabled an amendment to the EU Withdrawal Bill on Thursday following crunch talks with pro-EU Conservative backbenchers.
The group, spearheaded by former attorney general Dominic Grieve, are demanding a greater say for the House of Commons in the event the prime minister fails to agree a Brexit deal with the EU.
Ministers have resisted accepting their demands wholesale, having warned against tying Mrs May’s hands in negotiations with Brussels.
The peace talks broke down spectacularly on Thursday afternoon, with the government’s attempt at a compromise agreement immediately junked by the Tory rebels.
They also accused the prime minister of backtracking on promises made earlier this week.
As an insurance policy, Mr Grieve asked for an original amendment of his to the EU Withdrawal Bill, on the demands for a more “meaningful vote” for MPs, to be tabled in the House of Lords.
It is now likely peers will return the Grieve amendment to the House of Commons, setting up a parliamentary showdown on Wednesday.
One pro-EU Conservative warned the prime minister she is nearing the point where she will have to choose between the warring Remain and Leave sides of her party.
Mrs May only avoided a rebellion on the EU Withdrawal Bill this week when ministers promised to “engage positively” with rebels’ concerns and table a compromise amendment when the legislation returns to the House of Lords on Monday.
Explaining why he is opposed to the government’s compromise amendment, Mr Grieve told Sky News the unamendable nature of ministers’ proposal is “not a satisfactory state of affairs”.
It has been suggested, in the event of there being no Brexit deal or parliament rejecting a UK-EU agreement, MPs want the ability to be able to instruct the government to return to negotiations, extend Article 50 talks, or even call a second EU referendum.
However, Mr Grieve stated his group of pro-EU Tory backbenchers are “not going to rush” a decision on their next steps, as he stressed a need to be “sensible”.
Fellow Brexit rebel Anna Soubry accused the government of having altered a compromise agreed earlier in the day.
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.
Former pensions minister and Tory peer Baroness Altmann, who is reported to have recently attended an event with groups calling for a second EU referendum, told Sky News the government’s proposal was “extremely disappointing”.
She said: “This is a fundamentally different amendment that doesn’t respect what the House of Lords sent back to the Commons and doesn’t seem to reflect what Dominic Grieve’s amendment – that the government asked him not to put to a vote in the Commons, would have achieved.
“Effectively what we’re talking about here, is making sure that parliament has a meaningful say on the future of our country on what is probably the most important piece of legislation that we have had since the War.”
Baroness Altmann predicted the House of Lords will return Mr Grieve’s original amendment to MPs next week during the EU Withdrawal Bill’s “ping pong” between the two chambers.
Warning there is “clearly enough support” to pass Mr Grieve’s amendment, she added: “Maybe there comes a point where you can’t please everybody – and the different views are so diametrically opposed – there has to be an opportunity, perhaps for this to be properly tested, rather than fudged.
“And if that opportunity is within this bill on this particular amendment, we will see.”
Solicitor general Robert Buckland, who has been leading the government’s efforts at reaching a compromise with rebels, admitted ministers’ amendment isn’t “precisely” what the backbenchers had been asking for.
But, he denied the government had misled the MPs, telling Sky News: “They’ve been involved in the process as have other colleagues and, in the end, a decision was made by the government to table the motion in these terms.
“I’m sorry if they’re disappointed by the final terms of it.”
Labour’s shadow Brexit secretary Sir Keir Starmer told the government their amendment is “simply not good enough”.
“Theresa May has gone back on her word and offered an amendment that takes the meaning out of the meaningful vote,” he said.
“Parliament cannot – and should not – accept it.”
A spokesperson for the Department for Exiting the EU (DExEU) said: “We have listened to those across the House who called for the ability to express their views, in the unlikely event that our preferred scenario did not come to pass.”
DExEU set out three scenarios in which the government’s amendment would trigger a vote in both Houses of Parliament.
These are if Parliament rejects a Brexit deal; no agreement can be reached with the EU; or if no deal is agreed by 21 January next year.
The spokesman added: “This ensures that in all circumstances Parliament can hold Government to account, while also allowing Government to deliver on the will of the British people as expressed in the referendum.
“But this remains hypothetical and the Government is confident we will agree a good deal with the EU which Parliament will support.”