The Prime Minister's official spokesman said: "We have made good progress in the negotiations in relation to the withdrawal agreement but there are substantial issues still to be overcome in relation to the Northern Irish backstop".
But Labour's Brexit spokesman Keir Starmer again pushed back against the idea on Sunday, saying there's no obligation for members of Parliament to surrender to a bad deal out of fear of crashing out of the European Union without one.
As the talks ground to a halt, Ms. Critics of the Prime Minister, including from within her own party, believe the deal is shaping up to leave Britain at a disadvantage compared to unilaterally leaving without a deal and trading on World Trade OrganiZation rules.
To make matters worse, four more Remainer ministers are said to be on the brink of quitting, after Boris Johnson's brother Jo walked out demanding another referendum to reverse the whole process. "These are terms that might be enforced on a colony", he adds.
The European Union has been urged to remain "steadfast" over its guarantees to Northern Ireland by pro-Remain parties.
An EU diplomat said earlier on Saturday that they were cautiously hopeful that an EU summit could happen this month to endorse the deal but that the volatile situation in Britain made it very hard to predict.
Officials are trying to nail down what May called "significant" remaining issues.
In Belfast, Fine Gael Senator Neale Richmond, journalist Susan McKay and Ben Lowry of the Belfast News Letter joined Ms Byrne, while in Dublin, Mr Nolan was joined by the leader of Traditional Unionist Voice Jim Allister, Sinn Fein's David Cullinane, Alliance Party leader Naomi Long and Conservative MP Chris Chope.
Former prime minister Gordon Brown said Britain should leave the door open to rejoining the EU.
May still needs to convince her ministers and the parliament to go along with her vision of the deal for Brexit, due next March, despite the outstanding issues in talks with Brussels, notably over the Irish border.
Both the European Union and the United Kingdom need an agreement to keep trade flowing between the world's biggest trading bloc and the fifth largest national economy. May by insisting that she accept the EU's backstop proposal.
Johnson, who has on occasion been seen as a potential leadership candidate for his party and nation but has repeatedly failed to act at decisive moments, continued: "We have agreed to become the punk of Brussels, signing up not just to their existing rulebook but to huge chunks of future regulation - even though we will have no say in drafting that legislation.... We are not commenting further on leaks in the media".
RTÉ News understands that while the main backstop focuses on a UK-wide customs arrangement, there will be specific provisions within the text and within annexes for Northern Ireland, should the UK-wide arrangement not prove sufficient to avoid a hard border. "We assess the probability of a deal to trigger the status quo transition period as at least 70 percent".
Ms Foster has previously described the union between Northern Ireland and the rest of the United Kingdom as her party's "guiding star". But comments from a number of senior Conservative politicians backing a post-Brexit deregulatory drive, coupled with the Treasury's opposition to binding environmental targets and a robust United Kingdom green watchdog, have fuelled fears United Kingdom environmental rules could be axed once the country leaves the EU. However, DUP Leader Arlene Foster has also raised concerns about Ms.