The Labour Party and others, including the DUP, said that the vote is so important for the future of the country that lawmakers should be able to see any detailed legal warnings concerning parts of the withdrawal agreement.
MPs on Tuesday also voted to approve an amendment tabled by Conservative former attorney general Dominic Grieve, which allows parliament to determine what happens if the deal falls.
Chief whip Julian Smith acknowledged he faces an "uphill challenge" to persuade MPs to back Mrs May's deal, but insisted that "it's all to play for".
"They've been negotiating for two years and they got the deal".
Under the current deal the "backstop" would come into effect at the end of the Brexit transition period, which is due to last until the end of 2020 but may be extended.
The legal advice confirmed that Britain can't unilaterally opt out of the backstop, which requires an agreement by both sides. We can give more people the tools to decide for themselves what to believe.
"But, in the backstop we have no financial obligations, we have no free movement, we have very light level playing field rules with the EU".
She said: 'Really, the Norwegian option is not an option.
She said: "I want to build the broadest possible consensus both within this House and across the country, so for the next stage of negotiations we will ensure a greater and more formal role for Parliament". Which is why this week's debate in Parliament over the terms of withdrawal is crucial.
Mr Grogan (Keighley) said: "The deal the Prime Minister is offering us is reality a blind Brexit".
The DUP's Westminster leader Nigel Dodds said it would be "illogical" for his party to turn on the Tories if it had already seen off the Brexit deal.
The agreement is the only way to avoid a no-deal Brexit that would have dire consequences for the British economy and to head off those who are trying to use the debate to prevent the country from leaving the European Union, she said.
Changes could though be made to the political declaration on the future relationship if it helped get the deal through at a second attempt, one of the diplomats said. She issued a fiery defense of the deal in advance of the votes, warning that "Brexit could be stopped entirely" should the deal be voted down next Tuesday when it is scheduled to be voted on by Parliament.
"Consequently, I have decided the only honourable thing for me to do is to resign the party whip in Parliament".
Downing Street declined to comment on the speculation.
This would mean the European Union could "save face" as it could claim it hadn't renegotiated the withdrawal agreement but simply "tinkered with the non-binding political declaration".
"That's the risk that the Prime Minister is running", he said.
A source told the Press Association that Mrs May was "seeing a few members of Cabinet" but it was "nothing to get excited about".
Another possibility is Great Britain could leave the European Union with no deal, which could lead to economic chaos, not just in Europe but worldwide.
The symbolic vote - which was not supported by the Scottish Conservatives allied to May - was a rare example of near-unity on a constitutional issue in the nationalist-led devolved Parliament.
The legal advice, prepared by Geoffrey Cox QC, the attorney general, also makes it clear Northern Ireland and mainland Britain would be subject to different customs regimes under the backstop, creating a regulatory border in the Irish Sea.