There are whispers in Westminster and Brussels this evening that a deal could be on, with the main stumbling-block to an agreement - the Northern Ireland "backstop" now largely agreed by European Union negotiators, according to reports.
Earlier in the day May was forced into an embarrassing climbdown when ministers stated they would publish a "full legal statement" ahead of any parliament vote on the Brexit deal.
The measure would need to be approved by the European Parliament and EU member states to take effect.
Officials have said for weeks that agreement on divorce terms and a framework for future UK-EU relations was 95 per cent complete, and for several days negotiators have been meeting late into the night in Brussels in a bid to close the remaining gaps.
Cabinet ministers called to Downing Street to read draft Brexit documents.
Elaborating on the deal, "The backstop will come in the form of a temporary UK-wide customs arrangement, with specific provisions for Northern Ireland, which go deeper on the issue of customs and alignment on the rules of the single market than for the rest of the UK", RTÉ News' Europe Editor Tony Connelly wrote.
"I think it's the worst of all worlds", former education minister Justine Greening, who supported staying in the European Union in the 2016 Brexit referendum, told BBC radio, adding that she did not think there was any chance it could get through parliament.
Negotiations are continuing this week, but officials are warning unless there is dramatic progress by the end of Wednesday there is unlikely to be a summit this month to approve a Brexit deal.
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Mr Eastwood said: "The SDLP are glad to hear that an agreement might have been reached and we look forward to reading the text of that agreement in detail".
And Mr Russell was clear that while the Scottish Government still opposed the "chaos" of leaving the European Union, he added: "If Brexit is to happen, we have always said that co-operation between governments is clearly the right and best way both to ready our statute books and to agree common United Kingdom frameworks, where these are in Scotland's interests".
Irish broadcaster RTE reported that a "stable" text had been agreed on the thorny issue of the Northern Irish border.
Both Leave and Remain campaigners fear the deal - whose outlines are well known though it has not yet been made public - will be a limp compromise that fails to deliver either the letter or spirit of the Brexit the country asked for. EU-backing Liberal Democrats and the SNP are expected to vote against the deal.
However, EU sources suggest that they have moved all they can and that it is now for May to either accept the deal on the table or not.
"It's vassal state stuff as for the first time in 1000 years this parliament will not have a say over the laws that govern this country".
But as with all things Brexit, there are many obstacles to overcome.
Labour has also indicated it is likely to vote down the deal, though their MPs in areas which voted strongly for Brexit may abstain or vote with the government.