Mrs May's government and EU officials reportedly working non-stop to secure a new Brexit deal by Wednesday so it can be agreed by leaders in Brussels at the end of November.
Downing Street said talks had gone through the night – lasting until 2.45am this morning, with still "substantial issues to overcome".
The Prime Minister's plans are seemingly splitting her party down the middle, being criticised by both hard Brexiteers and pro-remain Tories.
Boris Johnson's younger brother Jo sensationally quit the Cabinet last week and laid into the PM's plans – going as far as calling for a second referendum.
And one Brexit supporting Tory MP today warned cabinet ministers that "judgement day is coming" and urged them to "defend their country".
“They will be judged on whether or not they had the moral courage to defend their country”
Mark Francois MP
Speaking on the BBC, Mark Francois MP said: "It is an open secret that there are five or six cabinet ministers that are very unhappy with Chequers.
“What they will do is up to them, but all cabinet ministers are going to be judged at the bar of history by what they do over the next few weeks.
“For them, they are at the apogee of the political system, judgement day is coming.
“They will be judged on whether or not they had the moral courage to defend their country, or whether a car and a red box and being called sir by a civil servant was more important than their nation's destiny.”
BREXIT: Theresa May's future at Prime Minister is now staked on Brexit (Pic: REUTERS)
Growing numbers of Tory MPs are warning Mrs May her Brexit plan will not be approved by the House of Commons.
Mr Francois said the PM's Brexit neogtiations had been "one tactical defeat after another".
Labour have also dug in their heels and said MPs will not allow the UK to leave with a properly neogotiated aggreement.
Jeremy Corbyn's Brexit spokesman Sir Keir Starmer said "technically" the whole Briext process can be stopped.
WARNING: John Whittingdale MP said Theresa May wouldn't last as PM if she can't secure a deal (Pic: GETTY)
CABINET: Penny Mordaunt MP warned Theresa May ministers could vote against her deal (Pic: GETTY)
Britian is set to leave the EU on March 29, 2019, and the next 48 hours are set to be critical to the process.
Both sides are hoping for a special summit at the end of the month to finalise the "divorce agreement" and thrash out the issue of the Irish border.
Mrs May's future at PM is now married to her succesfully pushing through a deal – with her strategy triggering a number of high profile resignations this year from within her own Cabinet.
International Development secretary Penny Mordaunt MP has warned the Cabinet could block any Brexit deal put forward by the PM.
RESIGNATION: Jo Johnson quit the Cabinet over Brexit and called for a second vote (Pic: REUTERS)
Boris Johnson claimed Mrs May is on the brink of "total surrender" to the EU over Brexit as he urged the Cabinet to mutiny against the Prime Minister's withdrawal agenda.
And another Brexiteer former cabinet minister, John Whittingdale, said it was difficult to see how Mrs May's premiership could continue if MPs rejected any Brexit deal she brought back to Parliament.
Pro-Brexit Commons Leader Andrea Leadsom added to Tory tensions by insisting the UK could not be "trapped" in a backstop agreement without the ability to leave at a time of its choosing.
Former foreign secretary Mr Johnson suggested that if Mrs May's plans for a backstop customs deal with the EU – aimed at preventing a hard border in Northern Ireland – went through, the UK could be reduced to the status of a colony.
PROTEST: Britain remains divided as the UK is set to leave the EU in March (Pic: GETTY)
The Prime Minister's spokesman said that he expected the Cabinet would continue to back Mrs May in the Brexit negotiations.
The spokesman said: "The Cabinet has backed the Prime Minister in moving forward with her negotiations with the EU and I expect Cabinet will continue to do so."
Earlier, Ms Mordaunt told Sky News: "The important thing is that there are two checks on this deal – there is Cabinet and there is Parliament.
"Cabinet's job is to put something to Parliament that is going to deliver on the referendum result.
"We need to work together as a Cabinet to do that. I am going to be supporting the Prime Minister to get a good deal for this country."
EUROPEAN UNION: Britain voted to leave the EU by a margin of 52% to 48% (Pic: PA)
Former transport minister Jo Johnson said he decided to quit Mrs May's Government because he was concerned at reports she was planning a publicity campaign which he said amounted to a "calculated deceit".
Reports suggested the campaign would compare the content of any deal secured by Mrs May with the prospect of a chaotic no-deal withdrawal, rather than comparing it to the UK's current situation as an EU member.
"This is a calculated deceit on the British people," Mr Johnson told the Evening Standard.
"I challenge the Government to come clean on the cost of Brexit. The reason they can't look us in the eye, it's because they know this will leave us worse-off and with less control. It's a gross abuse of civil service impartiality."