"The longer she leaves it, the easier it is for her to ram it through Parliament and say, 'it's my deal or no deal and you all know no deal will be catastrophic,'" said Catherine Barnard, professor of EU law at Cambridge University.
Upon her arrival at the EU summit, May told reporters: "We have solved most of the issues in the withdrawal agreement. There is still the question of the Northern Irish backstop."
The "backstop" refers to a commitment from both sides that even if Britain exits without a comprehensive deal, there will never be a hard border between Northern Ireland, which would leave as part of the United Kingdom, and the Republic of Ireland, which will remain part of the EU.
To ensure an open border - a stipulation of the 1998 Good Friday Agreement that brought an end to 30 years of sectarian violence - European negotiators have proposed that Northern Ireland continue to trade as a member of Europe's customs union.
Such an arrangement is anathema to unionists in Belfast and to May, who says it would cut Northern Ireland off from the United Kingdom.
May has proposed instead that the whole of the United Kingdom remain aligned with the customs union for a limited time. But that idea has been shot down by Europe's chief negotiator, Ireland's prime minister and members of her own party, who want the ability to do trade deals with the rest of the world. The Tory's chief whip told May yesterday that Parliament would vote it down.
Nonetheless, when May addressed Parliament today, she insisted that her compromise proposals were not dead.
After the Prime Minister made her renewed pitch in Brussels, she left the dinner so that leaders of the remaining 27 EU member states could discuss Britain's fate amongst themselves.
Although the summit had been billed as a "moment of truth," when a deal must be finalised to allow an orderly exit by Britain on March 29, the moment of truth has been delayed. European leaders are now discussing another summit in November - or even December before the holidays - to secure a possible accord.
Like May, European leaders continue to express confidence a deal can be struck - even as they are growing fearful of an unruly separation.
Arriving in Brussels, German Chancellor Angela Merkel echoed the European line that "90 per cent" of the withdrawal agreement was settled.
But in an address to the German Parliament earlier, Merkel revealed that her Government was stepping up contingency planning in the event that Britain leaves with no deal.
"This brings with it a whole array of questions, such as: How, the day after Brexit, do we manage the estimated 100,000 British citizens who, in some cases, have been living in Germany for years?" Merkel told German MPs.
The Chancellor said, "It is only fitting as a responsible and forward-thinking government leadership that we prepare for every scenario - that includes the possibility of Great Britain leaving the European Union without an agreement."
After Brexit talks broke down last weekend, French President Emmanuel Macron said on Tuesday, "I believe in our collective intelligence, so I think we can make progress."
But the French Government also published a draft of emergency legislation that would require Britons to secure visas to visit France if Britain leaves the European Union with no deal.
In a speech in London yesterday, John Major, a former Conservative Prime Minister, said the Brexit vote was a "colossal misjudgment" and that Brexit-backers sold the country a fantasy and would not be forgiven.
Brexit will "damage our national and personal wealth, and may seriously hamper our future security. It may even, over time, break up our United Kingdom. It will most definitely limit the prospects of our young," he said.
