"It's not practical, it's not desirable and it's not appropriate", Davis said.
But while Wednesday's votes seemed assured, May was under pressure over a promised compromise to quell a rebellion on Tuesday over handing parliament more say over any Brexit deal, with pro-EU lawmakers threatening to withdraw their support. The strained parliament session underlined deep divisions over Britain's European Union exit.
On the first day of votes that could further complicate her tortured negotiations to quit the European Union, parliament will debate a demand for a "meaningful vote" on any agreement May negotiates with Brussels before leaving the bloc next March.
Former deputy prime minister Damian Green wrote in the Sunday Express that the majority of the crucial votes would "pass easily".
A Tory Remain rebel has warned Theresa May that "if she f**ks us, she's f**ked, ' after Conservative MPs were given assurances by the prime minister that a compromise Brexit amendment to the 'meaningful vote" will be upheld.
"In all conscience, I can not support the Government's decision to oppose this amendment because doing so breaches such fundamental principles of human rights and Parliamentary sovereignty".
The change to the Government's so-called "meaningful vote" plan would mean that if MPs rejected the Brexit deal struck with Brussels, it would be Parliament which decides the future negotiating aims of the UK. It will be debated on Tuesday.
"Now it's Labour's turn to show its dysfunction", said one Labour lawmaker.
Party officials have been frantically lobbying to convince lawmakers who have threatened to vote against the government to stay in line, using arguments ranging from the threat of being turfed out by a government led by opposition Labour leader Jeremy Corbyn to losing leverage in Brexit talks with the EU.
The Totnes MP said she was "minded" to rebel to support a Lords amendment on giving Parliament a meaningful vote on an exit deal, telling the BBC: "We would like to see further concessions on the amendment on the customs union because it is just a very sensible amendment that says keep it on the table, don't completely rule it out".
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Once the ball was in a neutral area of the pitch, Gassama reviewed the decision and awarded the penalty. I think we just have to move on. "I was already thinking about how I would take it".
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After ministers' promised to compromise on his demands, Mr Grieve did not push his amendment to a vote and most pro-EU Tory MPs backed down from a potential rebellion on a similar House of Lords amendment to the bill.
Before the vote, she assured lawmakers she would honour her promise and deal with the "concerns raised about the role of parliament in relation to the Brexit process".
The parts of his amendment which he expects to be taken forward by ministers provide a mechanism by which Parliament has to be consulted by the end of November in the event of no deal or if a proposed agreement is rejected, he said.
Outside parliament, around 60 protesters called on parliament to stop Brexit, saying they were cheated by the 2016 campaign to leave the European Union which they suspected had been influenced by Moscow.
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.
It's an amendment that calls for the government to "take all necessary steps to implement an global trade agreement which enables the U.K.to participate after exit day in a customs union with the EU in the same terms as existed before exit day".
On Wednesday, parliament will consider a challenge to her commitment to leave the EU's single market and customs union, which will transform Britain's future trading relationships for many years to come. After losing her party's majority in parliament at an ill-judged election past year, she now relies on the support of a small Northern Irish party and the distance between victory and defeat is narrow.
Former home secretary Amber Rudd, a leading Remain supporter, and ex-party leader Iain Duncan Smith, a long-standing Brexiteer, warned defeat could lead to the fall of the Government.
The government was forced to give ground to pro-EU lawmakers in one key area, promising that Parliament would get more say over the U.K. -EU divorce deal.
"Partnership, love dance - don't care what you call it, that's what we will need to avoid any border to Northern Ireland", she said.