She had issued a plea for MPs to give her a clear "mandate" to reopen the Withdrawal Agreement which she agreed with the European Union last November and seek to secure changes to its controversial backstop provision. Amendment I wants a no-deal Brexit ruled out. "That is what most of us want to see - a negotiated settlement with the EU", Ms Morgan told the BBC Radio 4 Today programme.
"The prime minister said that in order to win the support of the House of Commons legal changes to the backstop will be required, that would mean reopening the Withdrawal Agreement", he told reporters.
The backbenchers believe that removing the immediate threat of a no-deal exit will weaken the prime minister's authority to try to seek concessions on the Irish backstop in Brussels and allow them to mobilise behind a plan that commands the support of MPs from across the Commons.
Weber said: "If there is now a unilateral attempt to reopen the agreement, the outcome will be that not just the backstop has to be renegotiated - then the Gibraltar question, the question of how much money Britain has to pay for exiting, the question of citizens' rights will have to be renegotiated".
Conservative lawmaker Nick Boles, who is backing an amendment created to rule out a no-deal Brexit and seek a delay to Britain's European Union departure, said that Tuesday "is probably the only opportunity that Parliament is going to have to intervene in this process, to take control".
May, who will meet with her cabinet on Tuesday, also faces major hurdles when her latest gambit is put to a test in a vote expected in the Commons later in the day.
If the European Union doesn't blink, then in two weeks time we will be back where we started, and the Parliament must try to work out [again] whether it wants May's deal, or to delay or cancel Brexit, or will just stare hopelessly at the oncoming no-deal Brexit.
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MPs would have been able to vote on delaying Brexit to the end of the year and preventing a no-deal exit under the terms of the Bill - although the Labour leadership said it would seek a shorter extension to Article 50.
"If the Prime Minister indicates in the debate that she will be pressing Brussels to reopen the WA to make changes to the backstop, I will gladly support the Brady amendment", he tweeted.
She said when she returns to Brussels she needs the strongest voice behind her, adding that the amendments "provide a cacophony of voices when we need just one".
Jeremy Corbyn said he would meet May to "find a sensible Brexit solution that works for the whole country", listing changes that his party wanted to see, but that May has shown no sign of supporting.
In an effort to appease those Tories who are proposing to back Boles and Cooper's plan to delay Brexit, May promised they would have another chance to vote to stop Britain leaving the bloc without a deal, according to people in the room Monday.
"The Labour Party will back the amendment tonight because to crash out without a deal would be deeply damaging for industry and economy", he said.
Conservative MPs have been instructed by the government to vote for Sir Graham's amendment, which could pave the way for a plan known as the "Malthouse Compromise".
In a statement, a spokesman said: "We welcome and share the UK Parliament's ambition to avoid a no-deal scenario".