Border talks decision will be the biggest call of Varadkar's career
Ireland is adamant that there must be no change to cross- border trade rules as Brexit talks go down to the wire.
Intense negotiations continued late into the night, with senior government sources in Dublin saying there was "less than a 50pc" chance of a deal today.
"We're not viewing today as a 'drop dead deadline'," said one source.
British officials were painting a more positive picture ahead of a crunch meeting in Brussels this afternoon between prime minister Theresa May and European Commission president Jean Claude Juncker.
Shortly after their lunch, Taoiseach Leo Varadkar will be briefed on the EU response to Ireland's proposals for the future of the border.
Mr Varadkar will then have to make the biggest call of his political career when deciding whether to accept the wording of an agreement or stall the talks further.
It is understood that the Irish Government has told the UK it does not need an in-depth plan for the future movement of people and goods to and from the North. However, it wants "a formal commitment" that there will be no "regulatory divergence" after Brexit.
It is understood that the text of an agreement, which was being worked on last night, runs to only a few pages.
"Essentially, the Irish Government is saying that, when it comes to areas like agriculture, education and medicine, the status quo will remain," said a source.
This is proving difficult to put into writing without the support of the DUP, which fears such a move will move the border into the Irish Sea.
DUP leader Arlene Foster said yesterday that Brexit will involve "a comprehensive trade and customs agreement" between the EU and UK.
"What is not sensible is proposing isolating Northern Ireland from its largest market," she said.
"It makes no sense to move the border to the Irish Sea and make trade with our biggest market - the rest of the United Kingdom - more difficult."
Mr Varadkar and Mrs May are expected to speak by phone before he chairs a special cabinet meeting at 9am today.
The Taoiseach and Foreign Affairs Minister Simon Coveney will seek opinions from ministers on how far to push the issue later in the day.
Sources say EU Council president Donald Tusk will phone the Taoiseach this afternoon to discuss progress on a draft agreement.
Mr Tusk had set today as the deadline for Mrs May to table her proposals, but sources in Dublin say there will still be negotiating in the days ahead.
"Everything is subject to change. We're looking for her to live up to the meaning of her Florence speech," said a source.
In that speech, Mrs May pledged to protect the Belfast Agreement and the Common Travel Area, but most significantly said the UK "will not accept any physical infrastructure at the border".
Ireland believes the only way this can be achieved is for the North to maintain its "regulatory alignment" with Ireland.
"We are looking for parameters within which a solution can be found in Phase II, and that is not an unreasonable ask," Mr Coveney said yesterday.
"We'd like a solution that involves all the UK acting as one but, if that is not possible, both governments needs to recognise that Northern Ireland had unique challenges."
Former UK prime minister Tony Blair has said the EU will not allow the continued free flow of goods across the border if Britain is outside the single market and the customs union.
He said only a "bespoke" arrangement on the island of Ireland would work.