Keir Starmer MP, Labour's shadow Brexit secretary, said: "At this critical stage, MPs can't be kept in the dark, nor can we risk parliament being bounced into a decision without having all of the facts available".
Speculation has grown about the concept of a "Plan B" - the path May will choose to take if her withdrawal agreement is voted down in parliament.
The likelihood of rejection could increase Monday if Labour is successful in forcing May to reveal the full legal advice she sought before agreeing the deal with European leaders last month.
MPs across Parliament have angrily accused ministers of ignoring the will of the House after they said they would only release a "full reasoned political statement" on the legal position.
Labour, obviously - but worryingly for ministers, Jeremy Corbyn's party says it has the support of the DUP, who prop up the government in the Commons, as well as the SNP and the Liberal Democrats.
Meanwhile, Mrs May is facing a battle on a second front with Labour threatening to combine with other parties - including the DUP - to force ministers to publish the legal advice given by Attorney General Geoffrey Cox.
The prime minister of the Netherlands is dismissing the idea that the European Union might revise the accord on its post-Brexit relationship with the United Kingdom. "I know it is challenging", he told the BBC on Sunday.
And Mr Gyimah, who until Friday was a science minister, said the government had a duty to "level with the public".
Some opponents of Brexit have campaigned for a new referendum giving voters the option to reverse Britain's 2016 vote to leave the bloc, although the government says no such new vote will be held.
"For the first time in more than 40 years we will have an independent trade policy", she will tell MPs.
Boris Johnson, who resigned from government over the PM's Brexit vision, described the arrangement in his weekly Daily Telegraph column as "a great steel trap that is about to clamp its jaws around our hind limbs and prevent our escape".
Prime Minister Theresa May began a day of meetings with foreign leaders aimed at strengthening the U.K.'s future trade ties as domestic opposition to her Brexit deal mounted.
Theresa May has clashed with Phillip Schofield over refusing to be pinned down to whether or not she would resign if her proposed Brexit deal isn't voted through. That's something May has said won't happen on her watch.
No 10 continues to try and arm-twist Tory MPs into voting for the Brexit deal next week, in the face of all predictions that they will fail.
Mr Javid told BBC Radio 4's Today the agreement on the terms of the UK's exit and its future relations with the European Union was "never going to be perfect" but it was the "right deal for the country".