Fellow politicians on Wednesday (March 20) criticised May, describing her conduct as "reckless" and "zigzagging all over the place".
The draft says the EU is considering delaying Brexit beyond 29 March, but it says no extension is possible beyond the European elections.
Germany's Minister of Foreign Affairs Heiko Maas attends a news conference with Finland's Minister for Foreign Affairs Timo Soini, Sweden's Minister for Foreign Affairs Margot Wallstrom and State Secretary for Foreign Policy of Denmark Jonas Bering Liisberg, in Helsinki, Finland March 19, 2019. May and the British Parliament.
"The choice that we have now is one of resolving this issue or extreme unpredictability", he warned.
After the defeats in parliament opened up the possibility of Britain leaving the European Union without a deal, May told parliament on Wednesday that she remained committed to leaving "in an orderly manner".
That fact, coupled with the continued intransigence of the DUP and Brexiteer Tory MPs, means that Mrs May just does not have the votes for her deal - ratcheting up the likelihood of no-deal unless something dramatically changes.
The Prime Minister said MPs had so far done "everything possible" to avoid making a decision on the way forward.
Others in the room told her that the Article 50 extension made it hard for them to support her deal if it came back to the House.
And she implored Brits to stick with her, saying: "You, the public, have had enough".
May told voters tired of a Brexit saga that has dragged on for nearly three years: "You want this stage of the Brexit process to be over and done with".
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She's likely to do that next week - within days or hours of Britain's scheduled departure - by arguing that circumstances have changed, and that the speaker's bar on a third vote no longer applied.
May's comments sparked immediate speculation that she was ready to resign if her deal was not voted through next week.
The European commission president, Jean-Claude Juncker, said the situation would "get easy" if MPs support the withdrawal agreement. The executive arm of European Union reportedly said on Wednesday that it would be politically and legally hard for the United Kingdom to extend its exit date by three months.
Pro-Brexit and pro-EU lawmakers are also unimpressed by May's divorce deal, and Parliament has rejected it twice by hefty margins. The envoys agreed that the statement will be friendly but tough, the person said, asking not to be named.
May asked in her statement what kind of message this would send to those who voted for Brexit.
In Parliament on Wednesday, May was accused of reneging on pledges she and her ministers made a week ago.
Another Labour MP, Diana Johnson, said she had seen Facebook posts calling for her, and other MPs, to be "shot and hanged".
In what was seen as a last ditch attempt to win over parliamentary support for her agreement with the EU, Theresa May delivered a controversial address from Downing Street where she suggested that a number of MPs are not on the side of the people over Brexit.
He said: "I think the Prime Minister has shown remarkable determination and resilience in trying to deliver on the referendum result through the unprecedented challenges of the scale of the task in the face of a minority government, so achieving consensus on any issue is extremely hard". "She spent most of her time castigating the House for its misconduct". Yesterday her government attacked their civil servants. Those who did attend said the premier showed no sign of budging.
Commenting on Mrs May's speech, he said: "This is a unsafe moment for the country".