Britain's negotiators, led by Brexit Secretary Stephen Barclay and Attorney General Geoffrey Cox, and EU leaders confirmed that the latest round of tough negotiations on Wednesday did not lead to any break in an impasse over the fate of the border between Northern Ireland and Ireland.
Talks between British ministers and the EU officials were described by both sides as difficult, with the EU going further and insisting there had been no breakthrough.
Brussels has insisted that there must be a legal backstop to prevent a hard border between British controlled Northern Ireland and the Republic of Ireland which is a member of the bloc.
The 500 km border between the two sides will be the only EU frontier in the British Isles after Brexit.
With a planned March 29 departure date looming, nobody knows how more than 640 lawmakers in Parliament will decide the result of May's proposals in a meaningful vote due on Tuesday.
The deal has already been rejected by a margin of 230 votes, the biggest defeat in recorded British political history.
Undaunted by that defeat, May has continued to press her deal, hoping that EU negotiators will agree on the Irish border issue.
If MPs reject May's deal again they will be given a vote next week on leaving the EU without a deal or delaying Britain's departure from the EU beyond March 29.
Political commentators predicted that EU negotiations usually go to the wire, and they expected that to happen in the Brexit negotiations.
Separately, Jeremy Corbyn, leader of the main opposition Labour Party, has been meeting Conservative MPs in a bid to win support for an alternative to May's Brexit deal. Many Labour MPs though want a second referendum to decide the issue.