Brexit-backing MPs have reacted angrily to the idea that the UK's transition out of the EU could be extended for another year, to the end of 2021.
No. 10 refused to rule out an extension after a summit of EU leaders in Brussels failed to make progress.
The move could buy the two sides more time to come up with a solution to the problem of the Irish border.
But the UK would have to pay billions more into the EU's budget and follow its rules for even longer.
Theresa May addressed her 27 European counterparts on Wednesday evening, urging them to give ground and end the current Brexit deadlock.
However, they said it was up to her to offer new ideas, and declared that insufficient progress had been made to call a special summit next month to draft a withdrawal deal.
Both sides did, though, agree to keep talking.
The UK is due to leave the EU on 29 March 2019 - but an agreement on how this will happen is proving elusive amid differences over how to prevent a hard border between Northern Ireland and the Irish Republic.
The UK has signed up to the principle of a backstop - an insurance policy designed to prevent the need for customs checks - but the two sides cannot agree over what form the backstop will take and how long it will last.
As it stands, the transition period - in which the UK would remain in the single market and customs union - is set to last until 31 December 2020.
The UK Parliament would have to agree to any extension and some MPs are warning that Mrs May will face a rebellion if she tries to do it.