The Prime Minister has called an emergency Cabinet meeting to discuss the details of the 500-page withdrawal agreement, with No10 said to be prepared for the possibility of resignations.
Ministers were last night briefed one by one on the contents of the draft divorce deal which has finally been agreed after months of protracted talks.
However former Brexit secretary David Davis said the UK had reached a "moment of truth" and urged his former colleagues to reject the proposals.
If the Cabinet approves the draft today, the EU's chief negotiator Michel Barnier would have to report to the European Council that "decisive" progress has been made before Donald Tusk can convene a summit, probably in the last week of November.
There, leaders of the remaining 27 EU states would be asked to put their stamp on the document.
The agreement would then be sent for ratification to both the Westminster Parliament and the European Parliament before a potential vote in the Commons on the deal before Christmas.
If there are any hiccups, a Commons vote would be delayed, making a No Deal scenario more likely, causing the Government to step up costly preparations for leaving the EU with no agreement in place.
The announcement that a draft text had been agreed has been met with open hostility from Tory Brexiteers and scepticism from Remainers.
And before a special Cabinet meeting this afternoon, Mrs May will face the Commons for a potentially tricky Prime Minister’s Questions.
"Cabinet and all Conservative MPs should stand up, be counted and say no to this capitulation," said Mr Davis.
Former foreign secretary Boris Johnson urged his ex-Cabinet colleagues to "chuck it out", warning on the BBC that the proposals made a "nonsense of Brexit".
Jacob Rees-Mogg, chairman of the influential European Research Group of dozens of Tory MPs, said: "It is a failure of the Government's negotiating position, it is a failure to deliver on Brexit and it is potentially dividing up the United Kingdom."
On the BBC's Newsnight, he said he had not called for a no confidence vote in Mrs May "but there comes a point at which the policy and the individual become so intimately connected that it will be very hard to carry on supporting this policy".
Asked if he would be writing a letter to the Tory backbench 1922 Committee about Mrs May's position, he said: "Not in the next 24 hours."
Ex-Tory leader Iain Duncan Smith suggested Mrs May's administration could collapse over the deal.
"If the Cabinet agrees it, the party certainly won't," he said, and when asked if the Government's days were numbered, added: "If this is the case almost certainly, yes."
Jo Johnson, brother of Boris and a Remain-supporter who quit as transport minister over the Government's approach, suggested that Cabinet ministers were questioning whether they could support the deal.
Asked if there could be further resignations, he told a rally in support of a second referendum: "I talk to many MPs, colleagues in the Cabinet and elsewhere ... I know how much they all think deeply about these issues and they are all looking deep into their consciences and thinking whether they can support this deal."
The special meeting on Wednesday could potentially be a flashpoint for tensions between Brexiteers and Remainers around the Cabinet table, with speculation that Leave-supporting ministers including Penny Mordaunt, Esther McVey and Andrea Leadsom could be prepared to quit if a deal ties the UK too closely to Brussels.
But sources close to Brexiteer ministers played down the prospect of walkouts, with Mrs Leadsom said to have enjoyed a "good discussion" with the Prime Minister.
Chief Whip Julian Smith told reporters: "I am confident that we will get this through Parliament and that we can deliver on what the Prime Minister committed to on delivering Brexit."
But the challenge of getting a deal through Parliament appears even more difficult for Mrs May than winning the support of her Cabinet.
The 10 DUP MPs, upon whom Mrs May relies for a majority, appear set to reject a deal if it crosses their red lines.
DUP leader Arlene Foster said: "I am heartened by friends of the Union on both sides of the House and across the UK who have pledged to stand with the DUP in opposing a deal which weakens the Union and hands control to Brussels rather than Parliament."
She added that "these are momentous days and the decisions being taken will have long-lasting ramifications" and pointedly stated that "every individual vote will count" in the Commons.
Scotland's First Minister Nicola Sturgeon said MPs must not fall for Downing Street "spin" that rejecting the deal means crashing out of the EU and "instead we should take the opportunity to get better options back on the table".
The deal follows intense negotiation in Brussels, with measures to prevent a hard border on the island of Ireland the main stumbling block.
Irish broadcaster RTE reported that the deal involved one overall "backstop" in the form of a UK-wide customs arrangement - as sought by Mrs May - but with deeper provisions for Northern Ireland on customs and regulations.
The Guardian reported that an independent arbitration committee will judge when a UK-wide customs backstop could be terminated.
There will also be a review in July 2019 six months before the end of the transition period, at which it will be determined how to proceed - a new trade deal, the backstop or an extension to the transition period.
The Daily Telegraph revealed that Attorney General Geoffrey Cox told Cabinet that Northern Ireland will be in a "different regulatory regime" under the customs backstop and subject to EU law and institutions, something that may "cross a line" for the DUP.
Labour leader Jeremy Corbyn said the party would vote against the deal if it failed to meet its tests.
"From what we know of the shambolic handling of these negotiations, this is unlikely to be a good deal for the country," he said.
But his own approach to Brexit will come under attack from former prime minister Tony Blair on Wednesday.
In a speech in London Mr Blair will lash out at the "abject refusal of the Labour leadership to lead the country out of the Brexit nightmare".