A joint legally binding instrument on the Withdrawal Agreement and Protocol on Northern Ireland confirming the European Union could not try to "trap" the United Kingdom in the so-called Irish backstop indefinitely was a key sticking point, she conceded.
The backstop effectively keeps Britain in the EU's customs union - and therefore unable to strike free trade deals with other countries around the world, ruining a key prize for staunch Brexit supporters.
Lawmakers rejected the deal 391-242, ignoring May's entreaties to back the agreement and end the political chaos and economic uncertainty that Brexit has unleashed.
In January the British Parliament rejected May's deal by 230 votes, the biggest defeat for a government in modern British history.
If the deal is shot down again by parliamentarians as expected, another vote will be scheduled for Wednesday, this time on taking the potentially calamitous option of a "no deal" Brexit off the table.
"If you pushed me to the end point where it's a choice between no deal and no Brexit".
Shadow Brexit secretary Sir Keir Starmer said Cox had confirmed that "no significant changes" had been secured to the Withdrawal Agreement and the government's strategy was "in tatters".
European Commission President Jean-Claude Juncker (R) and British Prime Minister Theresa May give a press conference following their meeting in Strasbourg, on March 11, 2019. If members of Parliament choose to veto a no-deal Brexit, they will then get a vote on whether to delay the U.K.'s departure from the bloc.
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Ranko Berich, head of market analysis at Monex Europe, said: "we are now back to a base case where May's deal is rebuffed and she is forced to seek an extension".
Many Eurosceptic Conservatives are likely to follow the lead of the Democratic Unionists, but Nigel Dodds, the DUP Westminster leader, requested more information about an "extremely important" third element of negotiations which had not yet been completed - a unilateral political declaration by the United Kingdom that the backstop was not binding.
Labour MPs have been calling for clarification on what will happen on March 29 - the day the United Kingdom is scheduled to officially leave the EU.
He described the texts as a "legally binding instrument on the Withdrawal Agreement and protocol on Northern Ireland and a joint statement to supplement the political declaration".
The EU said there would be no more negotiations with London on the divorce terms, struck with May after two-and-a-half years of tortuous negotiations.
More than two hours later - at 11:40 p.m. - the tired leaders sat down for a joint news conference to announce changes they both hope will now put an end to the tortuous negotiations that have defined the U.K.'s exit from the 28-country bloc.
"The prime minister has run down the clock and the clock has been run out on her", said Opposition Labour Party leader Jeremy Corbyn.