Donald Tusk, European Council President, on Thursday said May's idea that the United Kingdom could stay in the single market for goods after Brexit "will not work", and had been rejected by leaders of all 27 EU member states.
"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".
"It's even more true since they left the day after so as not to have to deal with it", he added, referring to top Brexit proponents.
Chancellor Angela Merkel agreed, saying the tone of discussions at the Salzburg summit showed the "atmosphere" of Brexit negotiations were improving. Until we do, we can not make progress.
"The Chequers plan can not be 'take it or leave it, '" he added.
"Europe isn't an a la carte menu", said French President Emmanuel Macron.
May was hopeful she would find enough support in the room to force Barnier into compromise - at least amongst the likes of Hungary and Poland, whose governments are not on good terms with the European Union leadership.
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.
European Union leaders will push for a Brexit deal next month but warned Prime Minister Theresa May on Thursday (20 September) that if she will not give ground on trade and the Irish border by November they are ready to cope with Britain crashing out.
"We need to compromise on both sides", said Tusk, highlighting the importance of the October 18-19 summit in Brussels.
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.
"There are positive elements in the Chequers proposal, but the suggested framework for economic cooperation will not work, not least because it risks undermining the single market", Tusk said.
The next major milestone in the Brexit process is fast approaching, with the October 18 summit labelled a "moment of truth" by Tusk.
For Ireland, it's important not to undermine the hard-won peace after decades of sectarian tensions in neighboring Northern Ireland.
Many business chiefs and investors say a so called "no-deal" Brexit would weaken the West, panic financial markets and block the arteries of trade.
The tone of some of their comments, particularly the irony of European Council President Donald Tusk, left May exposed at home as she heads into what is expected to be a tumultuous annual conference of her Conservative Party from September 30.
Currently, that's expected to last until the end of 2020 - but without a deal, Britain would crash out of the European Union on Brexit day, a development that in theory could see flights parked and trade between the two sides grind to a halt.