It appeared that the DUP's refusal to accept compromise language on the future of Irish border, under which the United Kingdom would commit to "continued regulatory alignment" to ensure a hard border would not return, was a hurdle too far.
May and European Commission President Jean-Claude Juncker fell short of a breakthrough, despite some encouraging progress on the Irish border issue.
"We will not accept any form of regulatory divergence which separates Northern Ireland economically or politically from the rest of the U.K.", DUP leader Arlene Foster said.
May and Juncker made no comment to reporters when they met at the European Union executive's Berlaymont headquarters for a lunch that diplomats and officials hope can seal a breakthrough that would open the way to negotiations on future trade relations.
But the two sides said they were within striking distance of consensus, setting up a hectic negotiating rush ahead of an European Union summit next week.
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White is facing a tight window to hire a new coach, with the first college football early signing period starting December 20. The players expressed excitement about Nebraska's future under Frost, and he shared those same feelings about his new team.
Border agreements are still being decided in the move towards Brexit.
Juncker described May as a "tough negotiator", and insisted that talks had not failed.
May hopes that her talks with European Commission President Jean-Claude Juncker and his Brexit negotiator, Michel Barnier, due to start at 1:15 p.m. (1215 GMT), can persuade her 27 fellow EU leaders that "sufficient progress" has been made on divorce terms for them to agree next week to open talks on their future trade relationship.
She said: "There are a couple of issues, some differences do remain which require further negotiation and consultation". "We have common understanding on most issues". But Ireland and the other EU nations are demanding to know how that will work if Britain is outside the EU's borderless single market and its tariff-free customs union, a looser trading bloc that includes non-EU states like Turkey. But then Northern Ireland's Democratic Unionist Party, which props up May's minority government, announced it wouldn't support any deal that made special rules for Northern Ireland. "I'm very confident that we will reach agreement in the course of this week".
May depends in parliament on a pro-British party in Northern Ireland that rejects any deal which would divide the province from the British mainland. "Getting closer to sufficient progress", he said. A British spokesman said: "With plenty of discussions still to go, Monday will be an important staging post on the road to the crucial December Council".