Back in January the two sides believed that the remaining nine and a half months would be enough to settle the remaining details of the UK's withdrawal deal and the outline of the post-Brexit trading relationship between Britain and the EU.
Dublin has signalled support for extending the UK's Brexit transition period in order to resolve Irish border issues.
The admission will anger Brexiteers in the Conservative Party and pose a particular challenge to Scottish Conservative MPs, who have argued strongly for a swift exit from the Common Fisheries Policy.
Her assessment was largely backed by her European counterparts, who were keen to talk-up the chances of a deal.
Antonio Tajani, the president of the European Parliament, said May offered them "nothing substantially new" to discuss.More news: Pakistan vs Australia, 2018: 2nd Test, Day 1 - Statistical Highlights
Asked by the Press Association if he was concerned that a hard border could result in a return to the Troubles, Gen Dannatt said: "I don't want to see a return to a hard border".
Nobody really wants Britain to crash out of the European Union without a withdrawal deal, but time is running out and the sides have bogged down over the contentious issue of how to manage the Irish border.
Despite suggestions that London would seek a one-year extension to the two-year transition, Downing Street would not be drawn on the idea. By working intensively and closely, we can achieve that deal. "I remain confident of a good outcome".
"There were no new proposals".
But Brussels feels the plan will need such complex policing and checking that it can not be sorted in time for agreement this month.
European Union leaders have recently suggested that the transition period, now due to end in December 2020, could be extended by a year to provide more time for a trade deal to be forged that would make the backstop unnecessary.
A final Brexit deal could now be put off until as late as December - beyond the point at which Mr Barnier had said an agreement was essential.More news: Ariana Grande Breaks Silence on Pete Davidson Split
Instead, a summit to seal a Brexit deal will only be called if and when the EU's chief negotiator Michel Barnier deems that there has been "decisive progress".
News that Theresa May might be prepared to delay Britain's departure from the European Union until the end of 2021 has caused fury on the front pages of several newspapers today. "It will most definitely limit the prospects of our young", he said.
"We are all doing our jobs and we are trying to get the best deal for this country, and that's it. Parliament is going to probably want to give some detailed instructions for the government and temper its approval with conditions".
But Keir Starmer, the Brexit spokesman for the opposition Labour party, said that lawmakers should be able to scrutinize and amend any government proposal.
The Shadow Brexit Secretary said: "That is not a meaningful vote and ministers can't be allowed to silence Parliament. Ministers can not silence Parliament", he said. "But the extended transition period could not be a substitute for a backstop".
"There is a real issue if this drags on that uncertainty drags on - we need a deal". Their lead picture is of Jean-Claude Juncker and Theresa May greeting one another with a kiss, with the fairly dramatic caption: "Is this the kiss of death?"More news: Iran says Trump cannot bring oil prices down by 'bullying