Chief Brexit negotiator Michel Barnier extended an olive branch in the lead up to the summit by saying the European Union would be willing to "de-dramatise" the issue of the Irish border, and that a "softening" of their position was possible.
The real interest will be whether the prime minister uses the statement to double-down on her Chequers plan or hint that there is longer a no path for the offer, which involves a free trade area for goods, governed by a common UK-EU rulebook.
In a press conference on Thursday after meeting with the EU27 leaders, Tusk was clear that May's plan to keep the United Kingdom tied to Brussels' rules on goods but not services was a non-starter as it threatens the integritiy of the Single Market.
That gives May just four weeks to come up with a new plan.
"Don't worry, be happy", joked EU Commission chief Jean-Claude Juncker after telling reporters after a summit in Austria that the Europeans had full plans in place in the event there was no deal before Britain leaves next March.
"Everybody shared the view that while there are positive elements in the Chequers proposal the suggested framework for economic cooperation will not work", he said.
Paul Whiteley, a professor of politics and government at the University of Essex, explains the latest on the unfolding Brexit process. Failing to do so could disrupt the lives of people and business on both sides, and undermine Northern Ireland's hard-won peace.
May tried to take the setback in her step, welcoming clarity on the deadline for a deal and promising to bring forward new plans on how to avoid a hard border in Ireland.
May said Britain and the European Union agreed on the need for a legally binding backstop to guarantee there would be no hard Irish border.
He also promised an offer to allay fears about a border being created between the United Kingdom mainland and Northern Ireland. "But I believe there is a willingness to a do deal".
She added: "There is still a lot of work to do", and a no-deal scenario can't be ruled out.
If it left without a deal, the country would move from seamless trade with the European Union to customs arrangements set by the World Trade Organization for external states. But she showed no sign of backing down from the proposals hashed out with her Cabinet at her country retreat of Chequers in July - so controversial with her own party that they provoked the resignation of her foreign secretary, Boris Johnson, and Brexit secretary, David Davis.
Brexit was pushed by those "who predicted easy solutions", Macron said.
Any Brexit deal will include a withdrawal agreement and transition period to smooth Britain's exit from the bloc.
Adding: "It's even more true since they left the day after so as not to have to deal with it".
This week both the Taoiseach and the Tanáiste Simon Coveney have stressed that talks can not be allowed to drift into the final months of the year.
"We are today at the moment of truth", Macron warned.