French President Emmanuel Macron said on Thursday the Brexit plan proposed by British Prime Minister's Theresa May was unacceptable in its current form and that he expected new proposals from Britain in October.
The Brexit action plan for EU leaders coming to Salzburg - briefed over and again in advance of the summit in off-the-record conversations with European diplomats - had been to spout words of support for Theresa May to help her secure an EU/UK Brexit divorce deal not just with Brussels, but with political opponents back home.
Asked if the EU's criticism of her plans increased the prospect that the two sides would fail to reach a deal, May said: "We are continuing to work for a good deal".
Despite all of this, May remained upbeat: she said the United Kingdom will "shortly" come forward with new proposals on the so-called Irish "backstop" arrangements for implementation at the border if no long-term solution is found.
On the issue of keeping the Northern Irish border open and "frictionless", to avoid a visible border that would risk reigniting old tensions, May said the UK's proposal was "the only serious and credibly proposition on the table for achieving that objective".
The UK Prime Minister told reporters she and Tusk had a "frank bilateral" with Tusk after the summit-closing press conference.
"Without a clear and precise solution for the Irish question and for the whole context of our future relations it will be hard to even imagine a positive process after October", he said.
"The Chequers plan can not be 'take it or leave it, '" he added.
Mrs May addressed EU27 leaders over wiener schnitzel with potatoes and Austrian wine, pitching her Chequers proposal before sit-down meetings begin on Thursday.
Six months ahead of Britain's planned European Union departure, calls within the country have been growing for a second referendum - backed by an expanding list of centrist politicians.
May's former Brexit minister David Davis has said up to 40 lawmakers from the Conservative Party will vote against her Brexit plans. "Now is the time for the prime minister to reset the negotiation and take Tusk's March offer of a free trade plus deal".
She maintains that the backstop would divide Northern Ireland from the rest of the United Kingdom in terms of customs after Brexit day in March.
Mr Coveney added: "What they are talking about is a de-dramatised minimum amount of practical checks that are needed so that the EU can ensure it protects the integrity of the single market and customs union".
After Wiener schnitzel and four hours of wrangling over Europe's migrant problem, May was given the floor and tried to win over her 27 peers by effectively asking them what they would do if they were asked to agree a "legal separation" of their countries - something she says the European Union is asking for by insisting Northern Ireland might stay under European Union economic rules.
In Mrs May's absence on Thursday, the 27 other European Union leaders will discuss issues including the UK's future relationship with the European Union and how to resolve the problems around the Irish border.
Mrs May also held a bilateral meeting with Irish premier Leo Varadkar at Salzburg yesterday morning, which was described by an Irish government source as "useful", with the Irish delegation emphasising that time was short and "we need to get to the stage where we can consider a legal text" on the backstop.
On Wednesday, Tusk announced a special Brexit summit in November, when he hopes a deal will be "finalized".
Labour leader Jeremy Corbyn said Mrs May had shown herself "incapable of delivering a good Brexit deal", and shadow Brexit secretary Sir Keir Starmer accused her of being "in denial". But he also said he thought there would be a deal.
Before setting off, her Downing Street office suggested that after she put forward new Brexit proposals this summer, it was now for Brussels to "evolve" its position.