But pro-EU Conservative lawmaker Dominic Grieve said that with the government's move "I am quite satisfied that we are going to get a meaningful vote on both "deal" and "no deal" scenarios.
These were the words of a minister expecting to win the vote.
During three and a half hours of tense debate on amendments to the EU Withdrawal Bill, government whips held whispered conferences with a handful of Tories on the Commons benches.
But Solicitor General Robert Buckland publicly implied that Government would be accepting part of Grieve's amendment, and said that a "structured discussion" would take place with rebels.
However, despite backing down, pro-Remain Tories signalled they would not be easily consoled by a compromise offered by ministers.
In a day of drama, May's position seemed suddenly weaker when junior justice minister Phillip Lee, who has always been critical of the government's Brexit strategy, resigned and said he would vote against the government.
Opening debate on the flagship EU Withdrawal Bill in the House of Commons, Mr Davis warned that the "cumulative effect" of a series of Lords amendments would "make it impossible to deliver the smooth and orderly exit we want".
Commenting after Tuesday's votes, Dr Lee said: "Delighted that the government has agreed to introduce an amendment to the EU Withdrawal Bill which will give Parliament the voice I always wanted it to have in the Brexit process".
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MPs were told that one parliamentarian had to be accompanied to a public meeting by a six armed police officers because of threats over their stance on Brexit.
Well what the Remainer MPs thought they heard from May does not seem compatible with Davis's red lines.
The government says the changes would weaken Britain's negotiating position and is seeking to reverse them in the Commons.
He said giving Parliament power to direct the government's hand in talks would be "an unconstitutional shift which risks undermining our negotiations with the European Union".
Despite depending on the votes of the 10 DUP MPs for her precarious Commons majority, there were signs of cautious optimism among ministers that they would get the numbers to see off the revolt.
But there is going to be no binary choice of the deal on the table or no deal, with Parliament bypassed.
"However, facing the prospect of a humiliating defeat, Theresa May has been forced to enter negotiations with her backbenchers and offer a so-called concession".
"We will put in front of Parliament the decision for them to vote. after that there will be a process of primary legislation to put the actual details of it in Parliament, so Parliament will actually decide on the application of the detail".
In what is likely to be a highly-charged appearance before the backbench 1922 Committee on Monday, the Prime Minister is expected to say that the way MPs vote will send a message.