The 27 leaders made abundantly clear to the British prime minister that the draft withdrawal agreement they reached after nearly two years of talks was not open to change.
Any meaningful alterations will come only in a separate treaty on future economic relations that the sides will begin discussing after Britain leaves the bloc on March 29.
Here are the four main scenarios facing Britain while the clock ticks down to the day it departs the European project after 46 years:
This is the Brexit that the British government and EU leaders want — and one which the British parliament refuses to accept.
The deal has been rejected from opposing wings of parliament for either keeping Britain tied too closely or remotely to the European Union.
May aborted a vote on the deal set for Tuesday because of its certain defeat.
Brexit backers in her party then plotted an ultimately unsuccessful coup that saw more than a third back a motion to force May out.
May promised them she would wring concessions from Brussels on Thursday and Friday.
But exasperated EU leaders told Britain to finally make up its mind about what it wants.
May’s government intends to reintroduce the very same draft for a vote some time between January 7 and January 21.
It will hope that fear of the chaos that a no-deal exit might bring will force lawmakers to put aside their reservations.
This is the doomsday scenario that threatens to trigger a recession in Britain and markedly slow the European Union’s economic growth.
May’s agreement was meant to keep trade rules between the world’s fifth-biggest economy and largest single market almost unchanged for a transition period running through the end of 2020.
A sudden shift to different standards would impact almost every economic sector — and possibly see the costs of everyday products in Britain soar.
Both sides have been forced to ramp up their preparations for a disorderly Brexit over the past few weeks.
UK businesses are stockpiling goods while Brussels is trying to find a way to maintain free-flowing operations involving London’s massive financial services hub.
Britons have been mulling another vote on their relationship with Europe since shortly after the first one backed Leave by a 52-48 margin in June 2016.
There is no law keeping Britain from doing it all over again.
Yet many question whether this would be democratic — and why a second attempt should take precedence over the first.
It also threatens to be just as divisive. Opinion polls show the country still split over whether Brexit is worth it or not.
Proponents are mostly EU supporters who argue that the Brexit people were promised looks nothing like the deal the sides have reached.
They add that Britons never backed a no-deal scenario and should be given the chance to opt out.
Opponents say that Britain cannot simply keep voting until people who like the EU get their way.
It is also unclear what options to give people in a second ballot — and what happens if Brexit wins again.
Britain appears to have two ways of still staying in the European Union.
The first would involve a referendum in which Remain wins.
The second could see the government decide on its own to revoke Article 50 of the EU treaty that lays out the process for leaving the union.
Leaders ranging from EU President Donald Tusk to France’s Emmanuel Macron have said in the past year that Britain would be welcomed back with open arms.
Yet May shows no signs of changing her mind.
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