"We can choose to leave with no deal, we can risk no Brexit at all, or we can choose to unite and support the best deal that can be negotiated".
Shadow Cabinet Office minister Jon Trickett said the Government was "falling apart before our eyes as, for a second time, the Brexit Secretary has refused to back the Prime Minister's Brexit plan".
European Union chief Donald Tusk has called for a summit of leaders to take place on November 25 so they can endorse a draft Brexit deal that has been reached with the British government.
Irish premier Leo Varadkar said the draft deal could provide the basis for a summit of European Union leaders by the end of the month, potentially on November 25.
It follows Brexit Secretary Dominic Raab resigning on Thursday morning after he told the Tory leader he can not support the Brexit deal she hammered out with the EU.
Speaking in Parliament on Thursday morning, May warned of the choice awaiting the United Kingdom.
The prime minister accepted there were "concerns about the backstop" solution to the Irish border question within the deal, which Brexit supporters said could keep Britain tied indefinitely into a customs union.
No.10 sources stress that while the legal Withdrawal Agreement is unlikely to be changed, the outline "political declaration" that accompanies it is clearly up for further negotiation.
"I am confident that this takes us significantly closer to delivering what the British people voted for in the referendum".
An embattled Theresa May vowed to fight on as UK Prime Minister Thursday in the face of intense opposition to her troubled Brexit deal, facing down a wave of resignations and demands for her to step down as leader.
Labour leader Jeremy Corbyn said the draft deal was "a failure in its own terms" and a senior spokesman said that the "likelihood" was that the party would vote against it in the Commons.
Raab, whose resignation was the most significant, said: "I can not reconcile the terms of the proposed deal with the promises we made to the country in our manifesto at the last election".
One eurosceptic lawmaker in May's Conservative Party said more colleagues were either putting in letters to trigger a no confidence vote in her leadership or were increasingly minded to do so.
Democratic Unionist Party (DUP) leader Arlene Foster said she expected to be briefed about the deal by May late on Wednesday, warning that "there will be consequences" if the leaks were true.
Corbyn insisted that Labour will "stop a "no deal" outcome" and work to bring a broken parliament and country back together.
May emerged from a five-hour meeting with ministers that had sent the value of the pound gyrating to announce she had full backing to move ahead with her Brexit plan.
In his resignation letter, Raab told May that it would give the European Union a "veto over our ability to exit".
Ranil Jayawardena, parliamentary private secretary at the Department for Work and Pensions, wrote in his resignation letter that the draft deal is not fair to those who voted to leave the European Union "taking back control of our laws, our borders and our money".
Asked if she was struggling to fill the two cabinet posts vacated by Dominic Raab and Esther McVey earlier on Thursday, she joked: "I have had, actually, rather a busy day". Sterling dropped 1.1% to 1.28 United States dollars and was 1.2% lower at 1.13 euros.
He praised the efforts of the EU's chief Brexit negotiator Michel Barnier, who was also present at the press conference.
"As much as I am sad to see you leave, I will do everything to make this farewell the least painful possible for both for you and for us", said Tusk, who in his role as European Council President chairs the meetings of leaders. "I therefore have no alternative but to resign from the government".
The parliament's chief Brexit official, Guy Verhofstadt, welcomed the draft deal as "the best agreement we could obtain".
May said she was sorry at the resignations and understood their unhappiness, but believed her deal was the right one.