"It's not practical, it's not desirable and it's not appropriate", Davis said.
The Prime Minister was expected to emerge unscathed on Wednesday from a second day of crunch votes in the House of Commons on the EU Withdrawal Bill. The strained parliament session underlined deep divisions over Britain's European Union exit.
Flashpoints include proposals to increase the power of parliament to decide on the final Brexit deal, and others seeking to keep Britain tightly aligned with the EU's economy after it leaves the bloc.
Some 13 Tories have signed a "soft Brexit" amendment to the separate Trade Bill, and it is thought that a few others may be considering breaking ranks.
British Prime Minister Theresa May faces knife-edge votes in parliament on her centrepiece Brexit legislation from Tuesday, despite her last-minute warning that defeat risked undermining her negotiations with Brussels.
May said the government would amend the bill to address legislators' concerns, but warned that "I can not countenance Parliament being able to overturn the will of the British people".
But it came at a cost - a government promise to strengthen Parliament's voice, potentially at the expense of its own power to set the terms of any final divorce deal with the EU.
The Labour whips - who enforce discipline in the party - instructed lawmakers Wednesday to abstain on an amendment favoring membership of the EEA.
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.
"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", she told the BBC.
Many lawmakers said it seemed likely that Britain would have to remain in a customs union with the EU, even though the government insists it will leave.
"If the Lords amendments are allowed to stand, that negotiating position will be undermined", she told them, adding that she was confident that "I can get a deal that allows us to strike our own trade deals while having a border with the European Union which is as frictionless as possible". The government earlier had said it would not support that amendment.
Theresa May's Brexit woes escalated today as justice minister Phillip Lee dramatically quit - accusing her of harming the country.
The "meaningful vote" will be the first major test after the House of Lords introduced 15 changes to the bill, trying to reshape the government's approach to Brexit by encouraging lawmakers to press for the closest possible ties.
But the latest maneuver by a minority government that has been forced to compromise with parliament anxious some lawmakers who feared it would hand the European Union an incentive to withhold any agreement on an exit deal to force a softer Brexit.
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 she lost the Conservative Party's majority in an ill-judged election past year.
May's minority Conservative government relies on the support of Northern Ireland's Democratic Unionist Party for a slender working majority in the 650-member Commons.
"The question of what form parliamentary approval of the withdrawal bill takes is one of the most significant decisions this house will have to take", he said.
"I think the big thing from the 1922 committee meeting is this - there is nothing that says unity more when you have to get two MPs, from different factions, to come out of the 1922 committee to brief the media and paper over the massive cracks between remain and leave Tory MPs".