When the Conservatives meet for their annual conference on September 30, they plan to push for May to ditch the Chequers plan, or face a challenge to her leadership.
European Council president Donald Tusk delivered the ultimatum at a press conference to conclude the summit.
“It must be clear that there are some issues where we are not ready to compromise, first off the four fundamental freedoms, the Single Market, this is why we remain sceptical of Chequers”, Mr Tusk said. She said the United Kingdom would shortly be bringing forward its own proposals.
But just minutes after he spoke, May insisted that her Brexit plan was the “only serious and credible” proposal on the table.
Some report that the Prime Minister has been left angry yet defiant following the rejection of her Brexit proposals, while other say she has been left fighting to save her plans – and her premiership.
Macron, meanwhile, expressed contempt for pro-Brexit British politicians who told the public there would be “simple solutions” to leaving.
If Theresa May hoped that a two-day summit with European leaders in the birthplace of Mozart would bring harmony to the fraught Brexit process, she will have left sorely disappointed.
But May says any Irish deal must hinge on the EU accepting her country’s proposal, which would – for a limited time – keep the United Kingdom in the European single market and customs union when it comes to trading goods.
The row comes ahead of an already hard Conservative Party conference for the prime minister.
“On the economic partnership, there is no solution that will resolve the Northern Ireland border which is not based on the frictionless movement of goods”, she said.
At an extraordinary press conference in Salzburg, Mrs May said she still believed a deal was possible, and offered a fresh concession on Northern Ireland – but acknowledged there was “a lot of hard work to be done”.
“It was clear today that we need substantial progress by October and that we then aim to finalise everything in November”, Merkel said.
A senior European Union source told Business Insider as early as June that May’s suggestions would not fly.
“If all conventional roads lead to a hard no-deal Brexit, the notion of Parliament exerting control and forcing another referendum on us would begin to look not wholly fanciful”, Peston wrote in the Spectator. “So don’t worry. Be happy, don’t worry”.
The UK and European Union are trying to reach a deal by mid-November and want to avoid a hard border – physical infrastructure like cameras or guard posts – between Northern Ireland and the Irish Republic but can not agree on how.
He told the BBC’s Politics Live: “It did not feel like the reciprocation of the statesmanlike approach that she (Mrs May) has taken”.
She needed to return with an acknowledgement from European leaders that her domestic critics were wrong and that they would accept Chequers as a basis for meaningful talks on a future relationship.
“As the government has repeatedly said, we are committed to implementing the result of the (2016) referendum and will not be revoking Article 50 (withdrawal clause)”, a spokesman said.
Mrs May’s Brexit proposals have come under fire from hardline Brexiteers within the Conservatives, such as former foreign secretary Boris Johnson.