Labour, the Liberal Democrats, the SNP and the DUP have all said they will vote against the government's deal, as well as many Conservatives.
Europe has largely held united through the negotiations, vowing that if Britain leaves their club, it must no longer benefit from club benefits.
The deal will nearly certainly come with steep costs for both sides, leaving leaders in the extraordinary position of negotiating a split that they nearly all believe will harm their citizens.
At a special summit in Brussels that was nearly derailed by a row over Gibraltar, the other 27 leaders will gather to sign off the agreement before May joins them to mark the milestone.
"The UK's position on the sovereignty of Gibraltar has not changed and will not change", she said.
"There is no plan B. This is the deal on the table and I'm not willing to contemplate defeat in the British Parliament because I have every confidence in Theresa May and the wisdom of the British people".
"If there's no agreement" over Gibraltar, said Sanchez at a press conference in Cuba, "there very probably won't be a European Council" summit.
The deputy leader of the Democratic Unionist Party in Northern Ireland has used a party conference speech to try to persuade Prime Minister Theresa May to change course on Brexit.
May has hailed the deal as the start of a new chapter for Britain, but European Commission President Jean-Claude Juncker said the U.K.'s departure was a tragedy.
"There is, between us - something - which are the remainings of love, " he said.
Gibraltar deal clears way for Sunday Brexit summit
Portugal's foreign minister said Saturday that he backed the Brexit deal, including Spain's request to have its say on Gibraltar's future.
Those who think that by rejecting the deal that they would have a better deal will be disappointed the first seconds after the rejection, " Juncker warned. I'm inviting those who have to ratify this deal in the House of Commons to take this into consideration.
She said that the draft agreement raises constitutional questions and instead insisted on "an outcome that does not leave Northern Ireland open to the perils of increased divergence away from the rest of the United Kingdom".
That included a plan being hatched by close allies such as finance minister Philip Hammond and work and pensions minister Amber Rudd, reported The Sunday Times without citing sources.
"If there was anything better I can tell you Theresa May would have gotten that", Dutch Prime Minister Mark Rutte told reporters.
However, that support is hanging by a thread over its opposition to May's plans for future ties with the European Union after Britain departs the bloc next March.
British MPs are most concerned about an arrangement in the withdrawal agreement to keep open the border between British Northern Ireland and Ireland, which could see the province follow European Union rules for years.
"This isn't about me", she said.
It said senior European Union figures are "war-gaming" how the bloc could extend Article 50 - the mechanism used to leave the bloc next March - to allow for various scenarios.
The small DUP has an outsize role because its support has been crucial to May's shaky government, which doesn't enjoy a majority in Parliament.
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.More news: Fight puts halt to Pusha T concert in Toronto