Theresa May told the potential rebels she would work to secure a "customs arrangement" with the European Union (EU), rather than remaining in "a customs union" as the House of Lords voted for in their amendment to be considered the House of Commons Tuesday.
Her minority government could easily be defeated on the customs issue if pro-Brussels Tories back the Labour Party and other anti-Brexit MPs, as well as on 14 other amendments to the EU Withdrawal Bill from Peers.
Five Labour MPs also rebelled by voting in favour of disagreeing with the Lords amendment: Ronnie Campbell, Frank Field, Kate Hoey, John Mann and Graham Stringer.
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.
Brexit campaigners still expressed concern that the concession may open the door to the European Union trying to force Britain into retaining the closest possible ties with the bloc by weakening the government's hand in the talks.
Asked what would happen if MPs rejected the deal, he said there would be no time to restart negotiations, with the United Kingdom leaving the European Union in March 2019.
"First, we must never do anything that undermines the Government's negotiating position or encourages delays in the negotiations", Mr Davis said.
Mr Corbyn's frontbench has already tabled amendments to the bill - as an alternative to one added by the Lords - aimed at delivering the same benefits as single market membership.
A Conservative MP has resigned from his ministerial role ahead of a crucial Brexit vote in parliament.
Until just a few days ago, it looked like members of Parliament would overturn key parts of May's Brexit plans - and in turn wield the power to bring down her government.
The Sun had a frontpage of British icons including Stonehenge, a fish and chip shop, a London bus and a football, saying "Great Britain or Great Betrayal". It also attacked the unelected nature of the House of Lords (which traditionally scrutinizes laws passed to it by the elected lower chamber), linking it to a perceived attempt to frustrate the Brexit process.
Theresa May saw off a revolt from the pro-European wing of her fractured party, averting what could have been a major political crisis. "The end of March 2019, we leave the E.U. Full stop".