Spain’s PM Pedro Sanchez restated his opposition to the deal, expected to be signed off by member states on Sunday.
No country can veto the deal on its own but the EU wants unanimous approval.
Theresa May has said a deal is “within our grasp” but her ex-Brexit secretary Dominic Raab said what was on offer was inferior to EU membership.
The prime minister will take calls on the BBC News Channel and BBC Radio 5 live later, in a special programme presented by Emma Barnett.
People can text questions to 85058 or use the hashtag #BBCAskThis ahead of the programme’s live broadcast between 12:30 and 13:00 GMT.
EU leaders are meeting to discuss both the legally-binding withdrawal agreement setting out the terms for the UK’s departure from the EU and the accompanying non-binding political declaration on the future relationship between the UK and EU.
The declaration has been heavily criticised by many MPs for lacking detail.
Mrs May addressed the media outside No 10 on Thursday after the European Council said the political declaration- outlining how UK-EU trade, security and other issues would work – had been “agreed in principle”.
“The British people want Brexit to be settled, they want a good deal that sets us on a course for a brighter future, and they want us to come together as a country and to move on to focus on the big issues at home, like our NHS,” said Mrs May.
“The deal that will enable us to do this is now within our grasp. In these crucial 72 hours ahead, I will do everything possible to deliver it for the British people.”
However, the future of Gibraltar remains a sticking point – Spain has long contested Britain’s 300 year-rule of the strategically important peninsula.
BBC Europe correspondent Damian Grammaticas said the EU was reluctant to let its unity fracture by pressing ahead without Spain’s approval, leaving diplomats to find a solution.
“What Spain is demanding is a clear statement added to the exit texts that any future agreement between the UK and the EU, such as a trade deal, would not apply to the territory of Gibraltar, unless the UK secured Spain’s explicit consent,” he added.
Late on Thursday, Mr Sanchez struck a combative note in a tweet, saying: “After my conversation with Theresa May, our positions remain far away…. If there are no changes, we will veto Brexit.”
Fabien Picardo, the chief minister of Gibraltar, said the territory was perfectly happy to have “direct engagement” with Madrid over future trade relations but would not be “dragged” or “vetoed” to the negotiating table when it had concluded the existing agreement in “good faith”.
Speaking on BBC Radio 4’s Today, he warned that if Spain sought last-minute changes to the withdrawal agreement, that would encourage British MPs and other EU countries unhappy with aspects of the deal to do the same.
Catherine Barnard, a professor of EU law and employment law at Trinity College, Cambridge, told the BBC that Spain’s room for manoeuvre was limited as the “divorce” document only had to be agreed at EU level by qualified majority voting, meaning 20 of the 27 member states.
“So Spain doesn’t actually have the legal power to block the agreement on the divorce,” she added.
The political declaration is a separate document to the 585-page withdrawal agreement, published last week, which covers the UK’s £39bn “divorce bill”, citizens’ rights after Brexit and the thorny issue of the Northern Ireland “backstop” – how to avoid the need for manned customs posts on the Irish border.
The withdrawal agreement is legally-binding, whereas the political declaration is not.
It sets out broad aspirations for the kind of relationship the UK and the EU will have after Brexit.
However, some of its wording is non-committal, allowing both sides to keep their options open, which drew criticism in the House of Commons.
Dominic Raab, who quit as Brexit Secretary last week, told BBC Radio’s 4 Today that the agreement would not be approved by Parliament as it would leave the UK bound by the same rules but without control over them.
He said the current proposal would be “debilitating” for the UK economy and the ability to negotiate independent trade deals would virtually disappear. He also questioned whether a new trade deal could be completed by the end of the transition period.
Speaking on Thursday, Labour Leader Jeremy Corbyn described the agreement as “26 pages of waffle” which “could have been written two years ago” while Lib Dem leader Sir Vince Cable, who is campaigning for another referendum, described it as an “agreement to have an agreement” that was “full of worryingly vague aspirations”
Conservatives Sir Nicholas Soames and Nick Herbert were among a handful of MPs to speak out in favour of Mrs May’s deal during the debate.
But many Tory backbenchers were unhappy. Philip Lee, who quit the government in protest at its handling of Brexit, said it “reads like a letter to Santa”.
Scottish Conservative MPs are also concerned that the declaration will not protect the interests of the UK fishing industry.
The SNP’s leader at Westminster, Ian Blackford, said Scotland’s fishing rights had been “thrown overboard like they were discarded fish”, adding, “so much for taking back control, more like trading away Scotland’s interests”.
But the government insists the UK’s “red lines” on fishing have been protected, and the text acknowledges the UK will be “an independent coastal state” with the rights and responsibilities that entails.
A government source said the EU had wanted “existing reciprocal access to fishing waters and resources [to] be maintained” but this had been rejected.
What happens now?
- Theresa May goes back to Brussels on Saturday for more talks with European Commission president Jean-Claude Juncker
- Negotiators try to get an agreement with Spain over Gibraltar
- EU leaders meet on Sunday to sign off on the withdrawal agreement and the political declaration
- If that is agreed Mrs May starts the process of getting MPs to back the deal – most are currently against it
- If MPs back the deal it then has to be ratified by the European Parliament.
- The UK leaves the EU on 29 March – and trade talks on the future relationship start.