“I fear we are reaching the limits of this process in this House,” she told MPs who voted her deal down again on Friday. Her remarks appeared to signal that she is prepared to call a General Election to try to break the deadlock.
Mrs May said the vote would have “grave” implications and that failure to support her plan was "almost certain" to involve an extended delay to Brexit, with the UK required to hold elections to the European Parliament in May.
Mrs May will not be able to bring her deal back to the Commons for a fourth attempt until MPs have taken part in the second round of a series of “indicative” votes on alternatives to the deal.
One idea being mooted at Westminster, was that if one option did emerge as a clear favourite there could be a final run-off vote with Mrs May's deal.
The Prime Minister is consulting senior ministers over the weekend on the way ahead after MPs voted on Friday to reject the Withdrawal Agreement by a majority of 58.
Following the defeat on what was supposed to be Brexit day, Labour called on Mrs May to finally accept that her deal was dead and to call a general election.
But Downing Street sources have made clear she has not given up hope of getting it through Parliament, despite having already suffered three crushing rejections by MPs.
One source pointed out that the scale of the reverse was significantly less than the previous occasions as a number of prominent Brexiteers, including Jacob Rees-Mogg, Iain Duncan Smith and Dominic Raab, fell into line.
"We continue to believe that the deal the PM has negotiated is the best outcome for the country and we will continue to seek a way forward," the source said.
However Nigel Dodds, the deputy leader of the pro-Brexit DUP, who Mrs May had been hoping to persuade to back her deal, said he would rather remain in the EU than support it.
"I would stay in the European Union and remain rather than risk Northern Ireland's position (in the UK). That's how strongly I feel about the Union," he told BBC2's Newsnight.
On Monday, MPs will stage a second series of "indicative" votes on alternatives as backbenchers, led by Tory former minister Sir Oliver Letwin, again take control of Commons business from the Government.
In the first round of votes on Wednesday none of the eight options considered - including a customs union with the EU and a "confirmatory second" referendum - was able command a majority.
However discussions between the various groups of MPs involved were expected to take place over the weekend to see if they could coalesce around one of the various proposals - most probably for a "softer" Brexit.
Rebel Conservative Brexiteers who backed the deal on Friday did so because they feared that - with the pro-EU Commons taking control - the alternatives were either a much softer Brexit - or no Brexit at all.
In Europe, however there was alarm that, with time running out, the UK was heading for a no-deal Brexit.
The result of the vote means that the Government has missed an EU deadline to secure an extension of the Brexit process and leave with a deal on May 22.
Mrs May now has until April 12 to go back to Brussels with new proposals and seek a longer extension to the negotiation process, or see the UK leave without a deal that day.
As European Council president Donald Tusk called an emergency summit for April 10, the European Commission said a 'no-deal' break on April 12 was now "a likely scenario".
Irish premier Leo Varadkar whose country is likely to be the remaining member state hardest hit by no-deal said that it was up to Mrs May to come forward with a plan to prevent that happening.
"It is not clear that the UK has fully understood that no deal is not off the agenda. Rather, it's a growing possibility," he said.
The German MEP Manfred Webber, an ally of Chancellor Merkel and a candidate to be the next head of the commission, said there had been "a failure of the political class in Great Britain - there's no other way to describe it".