European leaders paid respect to May's positive tone but said there had not been enough progress in Brexit talks to schedule another council summit in November.
The backstop is a proposed mechanism to keep the United Kingdom in the EU's Customs Union after Brexit - essentially precluding the country from taking back control of its worldwide trade policy - in order to prevent a hard economic border between the British province of Northern Ireland and EU member the Republic of Ireland.
At an European Union summit in Brussels, while the mood was more upbeat about the willingness for a deal to ease Britain's exit, several leaders and diplomats said May had offered nothing new to strike the kind of breakthrough needed to move forward.
If a withdrawal agreement is reached, a transition period would kick in after next March, which has been planned to end in December 2020.
There were still big gaps both in terms of shape of future trade relationship, but also on the backstop, he said.
Tusk advised May that "creative" thinking from Britain was required to avoid a hard border on the island of Ireland, the issue that has brought divorce negotiations to a standstill.
"There's lots of ideas floating around, it wouldn't be in the interests of getting to a deal for me to speculate", said Mr Varadkar.
The Prime Minister will briefly address the leaders of the European Union 27 on Wednesday evening before they discuss the state of play in the Brexit negotiations over a working dinner while she leaves.
"We are calling on people to step up and make it clear to Governments in London, Dublin and Brussels and across Europe that the views of the people of Northern Ireland are not represented by those who seek hard borders or a hard Brexit".
The Taoiseach said Ireland could look favourably on such a plan which would be helpful to everyone concerned as the implications of Brexit could require more time. "But we are defending the single market".
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Afghan officials and the Czech military say the attack took place late Wednesday in the district of Bagram in Parwan province. Afghan policemen stand guard at a checkpoint ahead of parliamentary election in Kandahar on October 18, 2018.
But with worst-case scenarios now seeming more likely, NPR's Soraya Sarhaddi Nelson reports, "European leaders say they are working on contingency plans for a United Kingdom departure from the bloc without a deal on how to manage critical issues like borders, customs and air traffic control".
The UK would continue to pay contributions to the bloc while having no say post-Brexit, deputy leader Nigel Dodds warned.
The taoiseach said he and the British prime minister were "in broad agreement" on the idea that the backstop could not be time-limited. "It doesn't resolve any of the underlying issues and keeps us in a painful Brexit holding pattern".
May had earlier addressed her fellow leaders, indicating that she could accept extending the post-Brexit transition phase to take the heat out the deadlocked issue of the Irish border, officials said.
They added: "We've always said that the transition should be as short as possible but as long as necessary".
However, Brexiteers have reacted with anger at suggestions the UK's stay within the EU's structures could be lengthened beyond what had previously been agreed as a 21-month period. "They do not know themselves what they really want".
Mr Corbyn said International Development Secretary Penny Mordaunt and Work and Pensions Secretary Esther McVey have refused to say they backed the Chequers plan, joking: "Maybe she could share a pizza with them and sort it out".
May pitched her vision of how to save the talks to European Union leaders left frustrated by a dramatic breakdown in negotiations on Sunday, just months before Brexit day on March 29.
European Council President Donald Tusk touches his eyebrow after delivering a statement during a joint news conference following a Tripartite Social Summit roundtable at the European Council headquarters in Brussels, Tuesday, Oct. 16, 2018.