The amendment in question hinges on whether lawmakers will get a "meaningful" vote on Britain's membership of the European Union.
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.
These were the words of a minister expecting to win the vote.
They reassured anti-Brexit MPs that the government would accept some of their core demands to give parliament a meaningful say on the terms of Britain's European Union divorce, including - potentially - a new deadline for a deal to be agreed with Brussels that could make it hard for the government.
Some lawmakers tried to shout him down and accused the government of wanting too much power.
The government will now enter talks with rebels about accepting a new amendment which would give MPs an effective veto on the Brexit deal May secures from the EU.
"The main reason for my taking this decision now is the Brexit process and the government's wish to limit parliament's role in contributing to the final outcome in a vote that takes place today", Lee, who voted to remain in the European Union during Britain's 2016 referendum, said on his website. The U.K. voted to leave the political and economic bloc of 28 nations in June 2016.
Despite many Conservative MPs who backed Remain in the referendum, just two rebelled against the government on a meaningful vote.
He said a concession of this kind would been "revolutionary" as the Commons can not override the government when it came to negotiating worldwide treaties.
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But while the well-worn arguments focusing on the nature of a meaningful vote were made, the real drama was taking place on the floor of the chamber where chief whip Julian Smith, solicitor general Robert Buckland and Brexit secretary David Davis as well as the Prime Minister's parliamentary private secretary (PPS) George Holingberry were in deep discussion with each other and Grieve, as they sought to avert an embarrassment for the government.
While promising "further discussions", he said he was concerned that empowering Parliament to "instruct" ministers what to do in the event of no deal would leave the United Kingdom in "very rocky constitutional territory". We had a personal assurance that we would find a way to address the concerns in the House of Lords when the Bill goes back there.
A statement from the Brexit ministry said the government had agreed to "look for a compromise".
"This needs to be resolved", Andrew Bridgen, a pro-Brexit Conservative lawmaker, told Reuters.
But the resignation by Phillip Lee, who has always been critical of the government's Brexit strategy, underlined the deep rifts in the party over Brexit that makes such votes anything but easy.
Details of precisely what this will involve will be agreed in the coming days when the bill is due to return to the House of Lords and ministers could table a fresh amendment.
If May is defeated in the House of Commons it will be yet another blow to a prime minister whose authority has been challenged several times since last year's election.
Fellow MP Antoinette Sandbach rejected suggestions by leading Brexiteers in her party that this would tie the prime minister's hands in negotiations.
The issue seen as most likely to provoke a rebellion was that of giving MPs a "meaningful vote" on the final Brexit deal.