The Prime Minister said during a press conference after the Salzburg meeting that she would not accept the EU's "backstop" plan to avoid a Northern Ireland hard border.
So how will the EU's major players go about solving a problem like Theresa?
These people do not respect any rules, they are the ones creating mayhem, not the rest of the community, he insisted and added that Europe is no "menu à la carte".
A combative Macron accused British Brexiters of lying about how easy it would be to negotiate an exit from the European Union on terms favourable to the UK.
Tusk stated in definitive terms that Theresa May's Chequers proposal would not work because all European leaders "shared the view [...that] the suggested framework for economic cooperation will not work - not least because it risks undermining the single market".
Earlier this year, a leaked European Union report accused Theresa May of "double cherry-picking", and branded the model set out in her Brexit speech in March as "unworkable". She said she doesn't think it's possible by the October council.More news: Ferry in Tanzania's lake Victoria capsizes - government agency
May responded to Musk's criticisms by saying that her proposals were "the only serious, credible" way to avoid a hard border with Northern Ireland.
Dutch Prime Minister Mark Rutte labelled the Brexit negotiations "a balancing act" and the leaders will have further opportunities to thrash an agreement out when they meet again in Brussels on October 18 and again in mid-November.
Like many leaders, including May, Tusk said, "We need to compromise on both sides".
Paul Whiteley, a professor of politics and government at the University of Essex, explains the latest on the unfolding Brexit process.
Labour MP Jo Swinson, from the People's Vote movement pushing for a second referendum on Brexit, said "Chequers is dead" and "whatever comes out of the negotiations now will inevitably be a very bad deal for Britain".More news: Christine Blasey Ford's family publishes letter of support
But this summit has now ended, leaving a decidedly bitter taste in the mouth and a sense that this will be a long and very hard autumn of negotiations with a real prospect of no deal at the end. If MPs rejected the Brexit deal, or no final deal was reached by January 21 next year, the government must table a statement on how it wants to proceed, and Parliament could use the vote that would take place on this as an opportunity to call for a referendum.
But she paid tribute to the "remarkable and astonishing" resilience of the Prime Minister, and backed her to reach an agreement that would avoid the United Kingdom crashing out of Europe without a deal.
Looming ever larger is the spectre of a "no deal" scenario - something that many Brexit supporters say could be tolerated, even welcomed by some - but which is widely seen by many economists and business people as catastrophic.
"The UK will leave on March 29 next year", she said over dinner, adding: "The onus is now on all of us to get this deal done".
May gave no indication that she would change her Brexit policy in Salzburg, and would not say that she believed that a no deal outcome was more likely after the embarrassing summit: "If we get to the position where there will be no deal, the British people can be confident we will be done what is necessary".More news: Russian Federation presents new proof that Ukraine downed MH17 flight in 2014