Democratic Unionist Party leader Nigel Dodds described it as "devastating" and said it made clear that the proposed backstop arrangement for the Irish border was "unacceptable" and must be defeated.
Speaking recently, he said: "I'm absolutely diametrically opposed to it and I'm assured by a very large number of colleagues that they hold a similar opinion". However this would cross a red line for May as it would continue freedom of the movement. In the implementation period we still have to negotiate the terms, but there will be concerns that there would be more money to be paid, for example.
Another fellow Cabinet minister, global trade secretary Liam Fox, also backed the deal, warning there was a "natural "Remain" majority" in Parliament and any attempt to overturn the 2016 referendum vote in favour of Brexit would be a "democratic affront".
The backstop is an arrangement created to ensure there is no return to a "hard border" between Ireland, which will remain part of the European Union after Brexit, and Northern Ireland when the United Kingdom leaves the bloc next March.
She suggested MPs could be "given a role" in deciding whether to activate the backstop, which is created to stop the return of a physical border.
During Prime Minister's Questions, East Londonderry MP Gregory Campbell accused the prime minister of allowing the Irish border to become a "negotiating ploy" by the European Union, adding that the backstop was based on a "false political assertion".
"The obvious, in terms of the role of the United Kingdom, is for it to be parliament that makes these decisions".
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'If a bad Brexit is forced upon our country and jobs and the economy are not protected, many of our people who have suffered from eight years of austerity will suffer even more, ' he said.
"The alternative is uncertainty and risk - the risk Brexit could be stopped, the risk we could crash out with no deal".
"The risk is that we end up with no Brexit at all". It is unclear what happens if the deal is rejected as Britain is due to leave on March 29.
"I think the Prime Minister has enormous goodwill on both sides of the House".
"If it can't, then I certainly would welcome the vote being deferred until such time as we can answer that question.' Mrs May's spokesman insisted the vote would go ahead as planned and she was simply 'taking stock" as senior ministers came and went from No.10 yesterday.
She said it would not be in the "national interest" to block the Withdrawal Agreement, adding: "The only certainty would be uncertainty".
"All week we have heard from Government ministers that releasing this information. could harm the national interest".
He said he had already been given authority by his local party's executive to submit a letter to Sir Graham Brady, the chairman of the party's backbench 1922 Committee, seeking a vote of no confidence in Mrs May. "Let's not create more division by going back for another referendum".