May, who will address EU leaders at the European council summit before dinner on Wednesday, as negotiators continue to grapple with the drafting of the withdrawal agreement, responded by insisting she would deliver a good deal, and condemned Labour for holding open the possibility of a second referendum.
First, no one with any experience of global trade negotiations believes that Britain and the European Union will be able to conclude the kind of uniquely ambitious trade and security partnership they say they want within the 21-month timeframe of the existing transition period.
May will address the other 27 European Union national leaders at a summit before they sit down to dinner without her. Officials said they expected the leaders to tell May they have little more to offer since talks stalled on Sunday and they will step up preparations for Britain to drop out of the bloc with no deal.
TRT World's Simon McGrgeor-Wood looks ahead to what could a be a tense gathering.
Summit chair Donald Tusk warned that the risk of a "no deal" dumping Britain out of the bloc and into legal limbo and border chaos on March 29 was greater than ever.
The issues relate to the "backstop" agreement demanded by the EU to avoid a hard border by keeping Northern Ireland within the European customs area.
May will meet one-on-one with Tusk at 5:45 pm (1545 GMT) before briefing her 27 European colleagues, but then the rest of the EU leaders will leave to discuss Brexit over dinner without her. And it might just help May by giving her the kind of political theatre useful in persuading Britons she has fought for the best deal. On Tuesday, officials echoed the mantra that "the clock is ticking" to agree a treaty that parliaments can ratify in time for Brexit.
At a three-hour British cabinet meeting on Tuesday morning, which included ministers with reservations about her strategy, May said a deal was possible if they all stood together.
Ministerial sources told Sky News "the most we can hope for is that they don't rule a November summit out".
Health and IT push Britain down global league table
Each indicator uses a scale from 0 to 100, to signify how close an economy is to the ideal state or "frontier" of competitiveness. Singapore is the most "future-ready" economy, according to the report, while Sweden has the most digitally skilled workforce.
Germany's Europe minister called on May to "take responsibility and be constructive".
Asked if the November summit would still go ahead, Mr Tusk said: "It's for the leaders to decide whether we need an extraordinary summit in November or not".
It comes as Tusk earlier this week warned European Union leaders that a no-deal Brexit is "more likely than ever before".
The diplomats said Barnier had revealed his offer to European Union ministers at a meeting this week in Luxembourg.
Both sides are now focusing on another summit in November, with the hope that differences can be squared at a further meeting before Christmas. Officials say that will include how to rush through emergency European Union legislation to cope with huge disruption to transport and trade links.
The plan was informally proposed to the United Kingdom during talks last week, the newspaper said.
Addressing MPs in the House of Commons on Monday, May had said a deal was "achievable" while sticking to her principles on the Irish border issue.
If they can't, then that leads to the question of what happens in the interim.