But the cabinet's anxiety about the nail-biting parliamentary arithmetic increased significantly after the resignation of Bracknell MP Phillip Lee, who left his post on Tuesday morning to free his hand to 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".
In this scenario, the government retains full control of Brexit's results, but also could mean a tougher exit.
Potential rebels fell into line after Solicitor General Robert Buckland said ministers were ready to "engage positively" with their concerns before the Bill returns to the Upper House next Monday.
In the event, Dr Lee abstained on the crucial vote, saying he was "delighted" the Government had agreed to introduce an amendment giving Parliament "the voice I always wanted it to have in the Brexit process".
Earlier this year, Lee had called on the government to release its economic impact assessments of Brexit and suggested the government change tack in talks with the European Union, underlining the deep rifts in his party over the best way to manage Britain's exit.
He responded: "I think Dominic Grieve's amendment makes a no deal Brexit more, rather than less, likely".
If the government fails to pass the bill as it is, it will be forced to change what it asks for in negotiations with the European Union -undermining May's position and possibly threatening her job as Prime Minister.
Kyrie Irving excited about Hayward's return, still noncommittal on future in Boston
However, Ainge would have to understand the risks of this move, especially when offering a package including Hayward. He's been a vital key for the Celtics and he's going to warrant somewhere between $12-14 million, per season.
A paper laying out the U.K. government position, due to be published this month, has been delayed because the Cabinet can not agree on a united stance.
Her fellow Conservative backbencher Stephen Hammond said: "Parliament must be able to have its say in a "no deal" situation".
Not at all. Among the many issues outstanding ahead of Britain's planned withdrawal date of March 29, 2019 is the question of what happens to the Northern Irish border.
It featured a British flag and the headline: "Ignore the will of the people at your peril".
Another flashpoint could come when lawmakers vote Wednesday on an amendment seeking to keep Britain in a customs union with the EU.
It is the legislation aimed at ensuring the United Kingdom has a smooth transition out of the EU.
Ministers have told rebel Conservatives they will agree to seek House of Commons approval for their course of action if no political agreement has been reached on the Withdrawal Agreement agreed with Brussels by November 30, which the original amendment had demanded.
Davis on Tuesday told the BBC, "that was the decision of the British people. and whatever we do, we're not going to reverse that".