Talks between Brexit Secretary Dominic Raab and EU negotiator Michel Barnier faltered on Sunday over the so-called Irish “backstop”, which could see the UK remaining in the customs union.
BBC political editor Laura Kuenssberg said no further talks were planned before Wednesday’s EU leaders summit.
But Number 10 said the government was still “committed to making progress”.
BBC Brussels correspondent Adam Fleming said Wednesday’s meeting would be dominated by the unresolved issues in the divorce process, rather than focusing on the future relationship.
He added that meant Brexit talks “might not be wrapped up in November, as the UK would like”.
This week’s summit comes as domestic political pressure on Mrs May increases amid threats of potential cabinet resignations.
And Labour’s shadow Brexit secretary Keir Starmer has heaped further pressure on Mrs May, calling for her government to publish its plan for the backstop.
Mr Starmer said any proposal needed full scrutiny from MPs before an agreement could be struck with the rest of the EU at the Brussels summit.
A Number 10 source said the prime minister had made sure Parliament was regularly updated on the talks.
Former Foreign Secretary Boris Johnson said the backstop idea should be jettisoned altogether.
Writing in the Daily Telegraph, Mr Johnson said that “in presuming to change the constitutional arrangements of the United Kingdom, the EU is treating us with naked contempt”.
Meanwhile, Ireland’s ambassador to the UK, Adrian O’Neill, said Sunday’s events in Brussels were a “setback” and could increase the prospect of a no-deal Brexit.
He told BBC Radio 4’s Westminster Hour that time was “running out”, adding: “Preparations for all eventualities are ramping up quite significantly.”
Is the PM out of moves?
By BBC political editor Laura Kuenssberg
While there may have been a sense in Brussels that Mrs May was moving towards them, if anything the politics at home have become more fraught.
Thursday’s cabinet meeting ramped up concerns and gave Brexiteers another excuse to rattle their sabres.
The DUP continues its warnings that it’d sink the administration rather than see the deal it fears done. Several cabinet ministers are thinking about whether they can go on.
And, more to the point, different groups of Tory MPs with gripes about other policies are scenting opportunity as the government is so vulnerable.
Any move for the PM has become both harder, and more urgent.
Her party won’t accept a proposal to keep the UK essentially in the customs union. Parliament is likely to block no deal. The EU won’t accept her Chequers plan.
Even loyal ministers are deeply worried – “She is like a chess player who only has the king left – all she can do is move one square at a time until she is check-mated.”
The issue of the border between Northern Ireland and the Republic of Ireland, which will become the UK’s border with the EU, is one of the last remaining obstacles to achieving a divorce deal with Brussels.
Wrangling is continuing over the nature of a “backstop” to keep the border open if a wider UK-EU trade arrangement cannot resolve it.
The EU’s version, which would see just Northern Ireland remain aligned with Brussels’ rules, has been called unacceptable by Mrs May and her Democratic Unionist allies.
The prime minister’s counter-proposal is for a temporary customs arrangement for the whole UK, but Tory Brexiteers fear this becoming an open-ended position that would prevent free trade deals with countries around the world.
In a letter to Mrs May, Scottish Secretary David Mundell and Scots Tory leader Ruth Davidson said they would not accept Northern Ireland being treated differently than the rest of the UK in any Brexit deal.
It follows reports that other top ministers have been considering their positions over the weekend ahead of a meeting of the cabinet on Tuesday at which ministers could be asked to give their consent to any agreement.
Writing in the Sunday Times, former Brexit secretary David Davis urged ministers to “exert their collective authority” and reject the plans at a cabinet meeting on Tuesday.
The febrile atmosphere in the Tory ranks has seen Mr Davis emerge as a potential successor to Mrs May.
Tory MP Nadine Dorries publicly suggested he could be the leader to deliver the kind of Brexit sought by Eurosceptics.
Ms Dorries said installing Mr Davis as interim leader “may be the only way to deliver Brexit and FTA [free trade agreement]”.