Chief negotiator Michel Barnier told French TV on Friday that 25% of the final withdrawal deal had still to be settled and it could still be derailed by disagreements over the border and other issues.
Dismembering Northern Ireland from the British economy is unlikely, at least while the British government is dependent on the support of the Democratic Unionist Party (DUP) for its parliamentary majority.
"There are always difficulties, and risks of a failure", said Barnier.
A No 10 spokesman said on Friday the United Kingdom did not recognise claims that its plans for the Irish border had been subjected to a "systematic and forensic annihilation" by European Union officials at a meeting this week with Britain's lead negotiator, Olly Robbins.
But one source told the Telegraph: "It was made clear that none of the UK's customs options will work".
It was a point that seemed to resonate with many Brexiteer MPs who have long argued that remaining in the Customs Union would prevent the United Kingdom from striking new trade deals with non-EU countries around the world.
But government sources did express exasperation at what they regard as the intransigence of the EU27.
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An EU source said there would be more talks in the coming weeks and opportunities for the United Kingdom to come back with fresh proposals ahead of June's summit.
Labour MP Stella Creasy, of the People's Vote campaign pushing for an European Union referendum on the final Brexit deal, accused Theresa May of "magical thinking" over the Irish border.
The EU27 negotiating team are frustrated that little has changed on the British side since last August, when they first rejected the government's proposals.
But in February, the European Union published a version which only included the third "backstop" option, which effectively draws a customs border down the Irish sea.
Pro soft-Brexit Conservative MPs believe the government may be deliberately presenting proposals it knows will be knocked back by Brussels, to help the prime minister break the deadlock in Cabinet about how to proceed.
The meeting threw serious doubt upon the deal United Kingdom and European Union negotiators are trying to strike on the terms of Britain's departure from the EU.
British Foreign Secretary Boris Johnson warned this week that there would be "very little point in Brexit" if the United Kingdom was not free to set its own tariffs. "I think Theresa totally gets that".
The development has put further pressure on the Prime Minister's plan to leave the customs union, which is also meeting resistance in both houses of Parliament.