The prime minister attempted to persuade European Union leaders in Salzburg last night that her Chequers plan was the "only credible" deal on the table.
"What we are proposing is a fair arrangement that will work for the EU's economy as well as for the UK's without undermining the single market", May told them. Tusk, meanwhile, said that the upcoming October summit would be the "moment of truth" for reaching a deal, and that "if the conditions are there" another summit would be held in November to "formalize" it.
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With Britain's departure from the European Union on March 29, 2019 looming, there are growing concerns that a deal on the post-Brexit relationship may not be cobbled together in time to ensure a smooth and orderly British exit.
May promised to bring forward new proposals that would ensure trade could move freely across the Irish border, but would not require different customs regimes in Northern Ireland and the rest of the United Kingdom, a key red line for the British Prime Minister.
- Dutch Prime Minister Mark Rutte said his country is better prepared for a no-deal Brexit than Britain and an agreement is "not easy" because of Mrs May's red lines.
Mr Tusk insisted that despite the EU's reservations about the Chequers plan, he is "a little more optimistic" about the prospect of a "positive outcome".
"Our industry is deeply integrated across both sides of the Channel so we look to negotiators to recognise the needs of the whole European automotive industry and act swiftly to avoid disruption and damage to one of our most valuable shared economic assets".
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Should a no deal be rejected by MPs as predicted, and with the Brexit date set in law for March 2019, the only feasible solution to solve such a constitutional crisis would be to either call a General Election or to refer to question back to the public in a second referendum before the March Brexit deadline.
She also hit back at whispers in Brussels of a referendum on the final Brexit deal, saying: "We all recognise that time is short but delaying or extending these negotiations is not an option".
Leaders had listened politely to May for a few minutes around the summit dinner table, laid in the Salzburg theater used in the finale of the film "The Sound of Music".
May is sharply constrained domestically on Brexit, both in her party and in parliament.
"Every day that is left we must use for talks", Tusk said.
Put differently, the problems with Chequers might be smaller than the problems of any other plan. In her own press conference, straight after Tusk's, she defended her proposals and gave no quarter to the criticisms that had been thrown at her. He also said there would be no second plebiscite on Brexit.
"But we all agreed on this today, the proposals in their current state are not acceptable, especially on the economic side of it", he said. And they made a decision to join the European Union with its rules.
Alongside politicians, a growing number of businesses, unions, and other groups have begun to support a People's Vote, including the Community Union, which is one of the main unions representing Tata Steel's workers in the UK.