She has to get any deal agreed with the European Union through Parliament, and the numbers aren't in her favor.
Speaking in Brussels, Barnier said a full customs union between the United Kingdom and the EU would solve the controversial Irish backstop issue as no new checks would be needed on goods crossing the border on the island.
"What we can not do is see the United Kingdom locked in via the backdoor to a customs union arrangement which would leave us in indefinite limbo, that would not be leaving the EU".
German economy minister Peter Altmaier said he is "convinced" a deal is possible after meeting worldwide trade secretary Liam Fox in Berlin on Thursday.
Media captionHelen Grant on the DUP: "I think they are bluffing".
The Democratic Unionist Party (DUP) is the other big issue for the prime minister, who relies on the Northern Irish party's votes to give her a notional majority in parliament.
Downing Street also announced a further 29 no-deal notices would be published on Friday afternoon, setting out what businesses and consumers should do in the event of there being no agreement by 29 March 2019.
"It does appear possible there will be a breakthrough", he said.
According to the BBC, Brexiteers were particularly concerned over the fact that Britain could be tied to the bloc's mechanisms indefinitely, which would become an obstacle to the country's independent trade deals elsewhere once it leaves the EU.
She reportedly pitched her solution to the Northern Ireland "backstop", a major sticking point in the negotiations that has bitterly divided her party and caused friction with the EU.
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The issue has become a major stumbling block in negotiations ahead of next week's crunch European Union summit in Brussels, ahead of which the bloc has called for "maximum progress" in talks.
The document stated that the government "expects" this arrangement to remain in place no later than the end of December 2021.
They have already sent warning shots by abstaining from an unimportant vote in the House of Commons earlier this week.
Northern Ireland would also remain in the single market for goods.
Finance minister Philip Hammond said there had been a "measurable change in pace" in talks in the last 10 days, but there were "some big differences left to resolve".
The head of the Democratic Unionist Party, Arlene Foster, said May "could not in good conscience" back an European Union proposal for checks on goods being imported to Northern Ireland from Britain after Brexit.
"I would advise them to hold firm against Brexit because either of these choices are unpalatable", he said at an event in London hosted by Reuters.
Boris Johnson, the former Foreign Secretary, said: "This is an important moment".
Other cabinet members, who appeared to not have been invited to the meeting, including Esther McVey, the work and pensions secretary, and Penny Mordaunt, the global development secretary, were said to be frustrated with the lack of a time limit, and, according to The Times, citing an unnamed source, were considering their positions.