But European Council president Donald Tusk stressed that economic aspects of Mrs May's Chequers proposals "will not work", while former Brexit secretary David Davis disclosed a "rock-solid core" of up to 40 Tory colleagues could vote against the Government's favoured approach.
Speaking directly to her counterparts at a dinner in Salzburg last night, the Prime Minister made it clear that if an agreement were not reached by the end of a special Brexit summit pencilled in for mid-November, the United Kingdom would not seek to extend the negotiations.
After receiving what she described as a "frank" briefing on the Brexit talks from Tusk, May gave a defiant press conference in which she insisted her plan was "the only proposal on the table".
There was "a lot of hard work to be done", she said, but added that the United Kingdom was also making preparations in case no deal could be reached.
On Tuesday the EU's chief Brexit negotiator, Michel Barnier, suggested that he was preparing to propose a new "backstop" proposal on the Irish border, attempting to "de-dramatize" discussions about what happens with Northern Ireland if Britain and the European Union fail to reach an agreement on a future relationship.
Warning that there was "less and less time" to reach a deal before the UK's March 29 2019 exit date, Mr Tusk confirmed he would propose an emergency EU Brexit summit in November.
And although Tusk told reporters there were some "positive elements" in the UK's blueprint, there is still no agreement on the Irish border.
Tusk, though, highlighted shortfalls in Britain's position on avoiding a hard border, as well as on economic cooperation, saying that "the U.K.'s proposals will need to be reworked and further negotiated".
The Prime Minister is expected to brief the other 27 leaders on proposals over dinner on Wednesday and they will then have a separate discussion on Thursday after she has left.
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Theresa May's Chequers deal has faced nearly unanimous rejection from Brexiteers and Remainers alike, after European Council president Donald Tusk said it "will not work".
As she notes: "After Brexit, the border between Northern Ireland and the rest of the island becomes the line between the huge European trading club and a country that's on the outside".
German Chancellor Angela Merkel said "there can be no compromises on the Single Market" and said "substantial progress" was still needed on the UK's Brexit plans. He admitted that the Chequers proposals forced him to compromise on some of his beliefs, but insisted the most important issue now was ensuring Britain left the European Union in "good order". (EU Brexit negotiator) Michel Barnier is doing well, he has our full support.
Specifically, he said that he would "clarify" which goods will have to be checked by customs officers as they are transported between mainland Britain and Northern Ireland.
It came after Mr Gove called on Eurosceptics to get behind Mrs May's Chequers plan by arguing it can always be adapted after Brexit.
The EU version of the so-called "backstop" would see Northern Ireland alone continue to follow many EU trade rules and regulations - but London says this would undermine the integrity of the UK.
Number 10 had not hoped for a breakthrough at this summit in Salzburg.
While some progress has been made in recent weeks on negotiations about the terms of the Brexit withdrawal agreement, negotiations over Britain's future relationship with the European Union remain stuck over May's plan to keep aligned with the European Union market in goods, but not in services. Both sides aim to reach a deal that solves the issue.
May says she can not accept having customs checks within the United Kingdom. We must do everything to avoid a hard Brexit.