Cooper's amendment seeks to shift control of Brexit from May's government to parliament and if successful could have a profound effect, giving lawmakers who want to block, delay or renegotiate Brexit a possible legal route to do so.If a subsequent piece of legislation is passed, it would give May until February 26 to get a deal approved by parliament or face a vote on whether to ask the European Union to delay Britain's exit to avoid leaving without a deal on March 29.
Downing Street also reiterated the government's objections to a separate amendment, tabled by Labour's Yvette Cooper and former Conservative minister Nick Boles, paving the way for an extension of Article 50.
Welsh MPs voted on party lines on Tuesday night.
"They cannot be changed, they cannot be nuanced, they cannot be renegotiated".
Amid the bitter wrangling Queen Elizabeth II appeared to make a rare foray into politics last week, emphasising in a speech the need for Britons to come together to "seek out the common ground".
Meanwhile, May is being urged to secure changes from the European Union to the Northern Irish backstop as part of her Brexit deal to get it past Parliament.
Ultimately though we expect Corbyn to back Cooper's amendment as the Labour leader has repeatedly demanded the prospect of a "no deal" Brexit be removed as a potential outcome.
Tory MPs were told at a meeting with Mrs May on Monday evening that they would be whipped to support the Brady amendment.
The backstop is part of the Withdrawal Agreement, and the Withdrawal Agreement is not open for re-negotiation.
If passed, the amendment could put pressure on Brussels to reopen the deal by offering a clear path through the current impasse.
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She added, "There is a very high risk of a crash-out, not by design, but by accident. the crash-out is the only scenario that does not require anyone to take any action or take any decisions". The backstop has been a sore point for many Tory MPs who argue it defeats the objective of Brexit, which was to leave the bloc as soon as possible.
"After the vote which is taking place now in the House of Commons in London, I hope that the British Government will rapidly present to our negotiator Michel Barnier the next steps which will allow the avoidance of a withdrawal without a deal, which no-one wants, but which we must all - despite everything - prepare for".
The speaker sparked outrage when he ignored convention and the advice of his clerks to approve the initial move forcing May to reveal her revised plan, which also gave MPs a motion on which to tag their amendments.
The prime minister's original Brexit proposals were thrashed by the parliament on January 15, with the government losing by record 230 votes.
"Members of the House of Commons have taken away the main negotiating card", he said.
"And Graham has said he could live with a protocol rather than changes to the text, whereas from our point of view there needs to be changes to the text".
In a change to previously announced plans, she will address MPs at the start of debate on a series of proposed amendments to the deal, urging them to back proposals from Sir Brady to replace the backstop with "alternative arrangements".
May believes her agreement can still win Parliament's backing if it is changed to alleviate concerns about the Irish border measure, known as the backstop.
"That will mean reopening the withdrawal agreement".
MPs voted 317 to 301 for May to seek new terms with the European Union over the thorny issue of the Irish border.
Speaking to Cabinet, she said she aims to return to the Commons "as soon as possible" with a revised deal, which will be subject to a "meaningful vote" of MPs.