It won't be lost on the prime minister that the decision of leaders at this European Council summit to effectively give her some space, means we've yet to get to those closing stages.
"We are not there yet. we will continue the work in the next weeks calmly and patiently", he said.
At the start of a summit that had previously been earmarked as the deadline for a breakthrough, both sides admitted the deadlock would take more time to untangle and said they were willing to extend the post-Brexit transition until the end of 2021.
Tusk also said the leaders expressed their resolve to stop the flow of illegal migration.
'The position is exactly the same for our Prime Minister. As the Financial Times has reported, they've proposed that Northern Ireland stay in the regulatory regime of the European Union for goods, allowing a free flow north and south.
"What Michel Barnier has indicated very clearly is that the European Union side, certainly, is willing to allow more time in the transition period to agree an alternative solution to a backstop", Mr Coveney told BBC Radio 4's Today programme.
"A further idea that has emerged, and it is an idea at this stage, is to create an option to extend the implementation period for a matter of months, and it would only be a matter months", she told reporters on the second day of an European Union summit.
She subsequently said that the United Kingdom had already put forward a proposal to avoid the need for either a hard border or a customs border between Northern Ireland and the rest of the UK.
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"I am open to the idea of an extension or a longer transition period, but that's not an alternative to a legally binding Irish backstop, so it's certainly not an alternative; it's something that might be part of the mix", he said.
Mrs O'Neill said: "In order to preserve her toxic alliance with the DUP, she is trampling over the rights of citizens by acquiescing to that party's refusal to share power (at Stormont) on the basis of equality".
She also faces a rebellion from her parliamentary partners, Northern Ireland's Democratic Unionist Party, which has threatened to vote against her government's budget if she concedes to the EU's demands over the backstop.
Ireland's premier has said that the key issue of agreeing the backstop deal is not only an issue of substance, but "an issue of trust".
Arriving for the second day of the European Council summit, Mrs May made clear she would accept an extension only as a means to ensure there was no hard border in Ireland if it proved impossible to implement the future partnership by the end of 2020.
"There is no reasonable solution yet over a hard border between Ireland and Northern Ireland", Roth said.
"I think where there is a will, there is a way", German Chancellor Angela Merkel is reported to have said, while it is thought the President of the EU Commission, Jean-Claude Juncker, told leaders May needs "help" to sell a deal back in Blighty.
May "urged businesses not to lose sight of the prize - that of a smooth trading relationship with the European Union alongside the ability to seek new opportunities and open up new markets with trading partners around the world", her office said.
Mr Varadkar said a longer transition period was not a substitute for a concrete agreement over the backstop. Now we know our limits: we don't want an agreement which calls into question the integrity of the single market, or the four freedoms, or which does damage to Ireland.
The chaos promised by "no deal" is very much in the minds of officials on both sides of the Channel. They do not know themselves what they want. Efforts to allay these objections, centred on fears of splitting the North from the rest of the United Kingdom, have run into trouble with the EU side who want to protect the single market and customs union.