The European Union Withdrawal Bill, a complex piece of legislation meant to disentangle Britain from four decades of EU rules and regulations, has had a rocky ride through Parliament.
The amendment would effectively give MPs the power to prevent the United Kingdom from opting to crash out of the European Union without a Brexit deal and is a major victory for Remain-supporting MPs in parliament.
Following a meeting with May, the conservative MPs said they had been promised input into the terms of a new Brexit deal if the first is rejected, while one minister said he would only commit to further discussions.
A Downing Street source said: "We will get a good Brexit deal that works for everybody in the UK".
In a highly charged atmosphere in parliament, lawmakers who oppose the government said they had received death threats and brandished a copy of one of Britain's tabloid newspapers, the Daily Express, which ran a headline saying: "Ignore the will of the people at your peril". "The end of March 2019, we leave the E.U. Full stop".
Labour MPs are expected to rebel against their party whip in significant numbers to vote in favour of a Lords amendment to keep the United Kingdom in a Norway-style trading arrangement post-Brexit.
MPs will spend a total of 12 hours debating and voting on 14 Lords amendments to the EU Withdrawal Bill - six hours on Tuesday and six hours on Wednesday.
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The House of Commons voted 324 to 298 to defeat an amendment to the EU (Withdrawal) Bill which would have removed her government's power to decide to leave the bloc without any agreement.
Hours before the debate began, a justice minister resigned in protest at what he called its "wish to limit" the role of parliament in shaping Brexit.
Opening the debate, Brexit Secretary David Davis insisted the government would abide by three principles to defend the will of the British people.
Theresa May saw off a revolt from the pro-European wing of her fractured party, averting what could have been a major political crisis.
"If it were to turn out there was a problem, we will deal with it".
Her fellow Conservative backbencher Stephen Hammond said: "Parliament must be able to have its say in a "no deal" situation".
Meanwhile, Tory Brexiteer Bernard Jenkin told the government he would not accept ministers agreeing to Mr Grieve's demand for the House of Commons to assume control of Brexit negotiations in the event of no deal.
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If May is defeated by a wide margin her position as Prime Minister could be threatened.
Asked about what had been promised, Mr Buckland, the solicitor general, said the government remained "open-minded" but he would not "blithely" commit to any changes until he had had those conversations.
He said a concession of this kind would been "revolutionary" as the Commons can not override the government when it came to negotiating global treaties.
The main point of contention between those who want to keep the closest possible ties with the European Union and those who aim for a clean break is a demand to give parliament a "meaningful vote" on any agreement May negotiates with Brussels.
Conservative lawmaker Phillip Lee, who had voted to remain in the European Union, resigned as the justice minister so he could speak out against the policy on Brexit.
They also voted to disagree with Lords amendment 37, which was part of an attempt to remove the exit day from the Bill and allow the Commons to rethink its approach.
United Kingdom government wins key Brexit parliamentary battle
Despite many Conservative MPs who backed Remain in the referendum, just two rebelled against the government on a meaningful vote. Other flashpoints in the parliamentary votes include proposals to keep Britain tightly aligned with the E.U.'s economy.