Theresa May was battling to keep her Cabinet together ahead of a crunch Brexit showdown at her country retreat.
Ministers will gather at Chequers to consider plans which could see the UK remain closely aligned to rules set by Brussels on agriculture and food, potentially making it much harder to strike a post-Brexit trade deal with the US.
Downing Street insisted it is "categorically untrue" that the post-Brexit relationship with the EU envisaged by Mrs May would make a trade deal with the US impossible.
The Prime Minister insisted the Government would secure a Brexit which would allow "ambitious" trade deals with the US, Australia and New Zealand.
But the plans led to open revolt among Eurosceptic Tory MPs, while Brexit Secretary David Davis is understood to have severe reservations about both the proposal and whether it could prove acceptable to Brussels.
Ahead of the Chequers meeting, which will see Cabinet ministers engaged in talks lasting all day and into the night at the Buckinghamshire retreat, the Prime Minister said the Government had "an opportunity - and a duty" to reach agreement.
"The Cabinet meets at Chequers ... to agree the shape of our future relationship with the European Union," she said.
"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 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."
On the eve of the Chequers meeting, Brexiteer ministers held their own private talks in Westminster.
Boris Johnson, Mr Davis, Michael Gove, Liam Fox, Esther McVey, Penny Mordaunt and Andrea Leadsom were involved in the talks.
A Cabinet source confirmed there was a "private meeting".
International Trade Secretary Dr Fox then spent 50 minutes in 10 Downing Street with the Prime Minister.
He left on foot, ignoring questions from reporters about his political future if the Brexit deal hampered the UK's ability to strike trade deals.