Senior Brexiteers, led by Boris Johnson, are understood to have met for private talks at the Foreign Office on the eve of a pivotal meeting at the prime minister's Chequer's retreat, where she will seek to unite warring ministers over her Brexit approach.
Ms May is expected to push her top team to agree plans that would see Britain remaining in full regulatory alignment with the EU on goods, but not services.
But her plans were thrown into fresh chaos on Thursday when documents circulated to ministers ahead of the Chequers summit indicated that the new approach would make it impossible to negotiate a US-UK trade deal - prompting a furious Brexiteer backlash.
David Lidington, the de-facto deputy prime minister, said he was "pretty confident" that colleagues would be brought into line but Brexiteers were expected to confront Ms May on the plans during the lengthy talks.
Former cabinet minister Nicky Morgan told Today: "What we cannot see is a position that is briefed out tomorrow morning and then over the next 48 hours members of the Cabinet start to undermine or query it or anything else.
"That is what we have seen before when the prime minister has made speeches and it's extremely unhelpful."
She said that cabinet ministers should adhere to the rules of collective responsibility, adding: "Everybody should be able to express their views very thoroughly as to what they think, but when they have come up with an agreed position, if somebody said, 'I just cannot live with this, this is not what I want,' then yes, I think that they would have to think about their position."
Mr Lidington said the prime minister was proposing a "common rulebook" with the EU on industrial goods and agricultural products "for good, practical reasons" such as preventing items like food from being held up at borders.
He said: "It will not be the European legislators or the European court that would be deciding the common rulebook.
"Any change to the rules is something that would have to go through parliament and be accepted by parliament."
He dismissed the "pretty selective leaks" of the plans overnight, comparing the details to a "dodgy theatre review".
Any suggestion that the plan would hit US trade deals was "categorically untrue", he added.
The Brexit wing of the Tories was in uproar last night over the proposals, as Eurosceptics believe it would keep Britain too closely aligned to Brussels.
David Jones, a Brexiteer former minister at the Department for Exiting the EU said Ms May's deal looked "not very good at all".
He said the prime minister had set red lines of leaving the customs union, single market and jurisdiction of the European Court of Justice, adding: "It does seem to me that all those three red lines would be breached by what is being proposed today."
Mr Jones added: "The point is that if we are making this commitment as the basis of a negotiation we will be expected to adhere to it, and whichever way we actually achieve that it is going to be something less than the full Brexit we have had repeated promises of by the PM and cabinet members."
The 22-strong cabinet was invited to Chequers, Ms May's Buckinghamshire retreat, with talks expected to run late into the evening. Ministers will have their phones and other devices confiscated, to prevent any documents being leaked.
Speaking ahead of the summit, Ms May said: “The cabinet meets at Chequers today to agree the shape of our future relationship with the European Union. In doing so, we have a great opportunity – and a duty. To set an ambitious course to enhance our prosperity and security outside the European Union – and to build a country that genuinely works for everyone.
“We have already made good progress – on the text of the Withdrawal Agreement, by passing the EU Withdrawal Act and in agreeing an implementation period which gives people and business certainty. Now is the time for another step forward.
"We want a deal that allows us to deliver the benefits of Brexit – taking control of our borders, laws and money and by signing ambitious new trade deals with countries like the US, Australia and New Zealand.
“This is about agreeing an approach that delivers decisively on the verdict of the British people – an approach that is in the best interests of the UK and the EU, and crucially, one that commands the support of the public and parliament.”
If Ms May does secure an agreement, her next hurdle will be trying to get it past the EU.
Senior figures in Brussels told The Independent that her new plan would be “dead on arrival”, as any hint that the UK wants to be part of the single market on goods, but not services will be rejected.
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