"We have made good progress in the negotiations in relation to the Withdrawal Agreement but there are substantial issues still to overcome in relation to the Northern Irish "backstop", that remains the case", May's spokesman said.
Pro-Brexit Commons Leader Andrea Leadsom added to Tory tensions by insisting the United Kingdom could not be "trapped" in a backstop agreement without the ability to leave at a time of its choosing.
Jo said that Boris, who led the Leave campaign, was "as unhappy with the government's proposals as I am".
Hope of getting the Cabinet to sign off on Brexit proposals on Tuesday appeared to be rapidly receding, as it was reported the European Union had rejected London's plans for an independent arbitration clause that could allow the United Kingdom to quit a backstop deal on the Northern Ireland border.
Home Secretary Sajid Javid, Defence Secretary Gavin Williamson and Chancellor Philip Hammond raised concerns about the Chequers plan, the BBC reported.
'I can't really believe it but this Government seems to be on the verge of total surrender, ' Mr Johnson said in his column for today's Daily Telegraph.
'On the present plans we will be a vassal state, and in the customs union, until such time as our EU partners may feel moved to enter into fresh negotiations on a trade deal.
Mr Johnson claimed that "even if the Cabinet mutinies - as they ought - it will make little difference".
Former culture secretary John Whittingdale, a Brexiteer, said Mrs May would have to quit if MPs reject any Brexit deal she brought back to the Commons.
A senior cabinet minister was quoted in the paper as saying: "This is the moment she has to face down Brussels and make it clear to them that they need to compromise, or we will leave without a deal".
Justine Greening said there was no chance that May's proposed Brexit deal could win a parliamentary vote, calling it the "worst of all worlds".
Hope of getting a deal for the Cabinet to sign off on Tuesday appeared to be rapidly receding, but talks are continuing in Brussels.
The apparent impasse makes it much harder for the PM to secure a special European Union conference in November to settle Brexit terms.
"We should be planning as to how we can put this final say in the hands of the British people", she said.
But in a sign of Downing Street attempting to push the process forward, Mrs May's key Brexit adviser Olly Robbins held talks with counterparts in Brussels over the weekend.