In the days before the summit, some states raised objections regarding the content of the withdrawal agreement, including over the issue of fishing rights in the UK's territorial waters post-Brexit.
That's because Spanish Prime Minister Pedro Sánchez insisted his country have final say over any future status of the enclave, a self-governing British territory on the tip of southern Spain and near the narrow mouth of the Mediterranean.
Germany´s Chancellor Angela Merkel (L) chats with President of the European Commission Jean-Claude Juncker during a special meeting of the European Council to endorse the draft Brexit withdrawal agreement and to approve the draft political declaration on future EU-UK relations on November 25, 2018 in Brussels. "We are all losing because of the United Kingdom leaving", Rutte said. "Spain achieves a triple armory with which it can definitively deal with the United Kingdom [over] the future of Gibraltar in the coming years".
Asked whether there was any chance Brussels would reopen the pact if an alliance of pro- and anti-Brexit forces votes it down in the House of Commons, Juncker simply stressed "this is the best deal possible" - although summit chair Donald Tusk sounded more guarded, saying he did not want to consider hypotheticals. He added: "No one has reasons to be happy".
The UK is scheduled to leave the European Union on 29 March 2019.
Her comments came as her former Brexit Secretary Dominic Raab said staying in the European Union would be better than leaving under Mrs May's deal.
But demands that extensive treaty documentation recently agreed between Brussels and London be tweaked to give Spain a bigger say over its implementation in regard to Gibraltar face resistance from Britain and European Union allies who are wary that the whole edifice of the long-negotiated deal might unravel.
On Saturday, as the dispute threatened to derail the summit, London issued a statement saying Number 10 would not use the withdrawal agreement as cover to cut short its dialogue with Spain.
"Throughout our history we've stuck with Britain", said Fabian Picardo, the Chief Minister of Gibraltar.
"Economics is not the only consideration - we also have to look at the political healing process, bringing our country back together because countries that are disunited and divided are not successful countries".
A diplomatic source said the minutes of Sunday's summit meeting of the 27 leaders would record those concerns, although it was not clear if they would be made public.
TRT World's Kevin Ozebek has more from Brussels.
Members of the British campaign group Our Future Our Choice were seen setting fire to a copy of the divorce document in the Belgian capital this morning, while others hacked away at them with scissors and shredded it into ribbons.
May met the presidents of the European commission, European council and European parliament on Saturday evening.
In a sign of the trouble ahead for the prime minister, former Conservative Party leader Iain Duncan Smith told Sky News today it would be "very, very difficult" to support the deal arguing "far too much has been given to the EU".
His comments came as the Prime Minister travelled to Brussels with her Brexit deal under threat at home and overseas.
"The Council and the European Commission reinforce therefore Spain's position, as never before, ahead of the most vital negotiations that we will have, because we will need to talk about co-sovereignty, among many other things, with the United Kingdom", the Spanish PM said.