The plan briefed to senior members of her cabinet including attorney-general, Geoffrey Cox aimed to finally solve the remaining issue of the “Irish backstop” with the bloc.
A whitehall source told the Sunday Times, Mrs May’s plan is the governments “life-support machine” adding: “By rejecting the proposal, the EU has just turned off the oxygen.”
Tory officials have insisted the Prime minister needs to get tough with Brussels ahead of the next round meetings with the EU27, which is expected to be later this month.
A senior cabinet minister said: “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.”
Former Brexit Secretary David Davis has urged the government to ensure the UK remains in control of “our destiny” during negotiations.
He said: “Taking back control of our laws and borders means that a sovereign UK parliament must be able to determine our future as a self-governing, trading nation. Our destiny must not be in the EU’s hands.”
Brexit-backing Commons Leader Andrea Leadsom, addressing the Irish border backstop plan, said the UK “cannot be held against its will” in a customs arrangement with the EU and claimed MPs would not support a scenario in which the UK could not decide when to leave.
Mrs Leadsom said: “It cannot be a decision that can be overturned by the European Union, it must be capable for the United Kingdom to decide to leave that customs arrangement and it cannot be something the European Union can hold us to.”
The EU’s proposal, to keep Northern Ireland in its customs union and single market would risk “destroying” Theresa May’s government which is propped up by the DUP (Democratic Unionist Party) according to former a Brexit minister.
Steve Baker, deputy chairman of the 80-member European Research Group, said: “If the Prime Minister proposes to allow the EU to split the UK, or leave us in the EU’s customs territory or regulatory system, she risks destroying what’s left of her government.”
Downing Street played down the crisis: “We are pushing hard and Brussels is pushing hard.
“This is what the end-stage of negotiations looks like.”