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 agreement was resoundingly voted down in January on the issue of the "backstop" is meant to avoid a hard border between Ireland (EU state) and Northern Ireland (part of UK), but many see it as an EU ploy to keep in the United Kingdom within the customs union and the single market.
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.
Brexit-supporting MPs had said they would look at what Mrs May achieved before the vote, but that she would have to show a clear way for the backstop to end. The U.K. won't be represented in the European Parliament after it quits the EU; its seats already have been given to other countries to fill in the elections.
Samuel Tombs, the chief United Kingdom economist at Pantheon Macroeconomics said on Twitter that it was "pretty clear" markets think Cox's legal advice didn't give enough cover for euroskeptic lawmakers to change tack.
May is hopeful that she can push her deal through in the parliament.
Even if they formally get on board, though, there will be a rump of super-committed Tory eurosceptics - both inside and outside the ERG - who will always vote against any version of May's deal.
"Now is the time to come together, to back this improved Brexit deal, and to deliver on the instruction of the British people", she said.
Bloody Sunday: families react to former soldier charged with murder
But family members said they were deeply disappointed that more paratroopers will not be charged over the incident. Papers before prosecutors included 668 witness statements and numerous photos, video and audio evidence.
The legal advice deals a significant blow to the prime minister's hopes of overturning MPs' 230-vote rejection of her Withdrawal Agreement in the second "meaningful vote" on the deal in the House of Commons.
Now that the House of Commons gave leaving the European Union without an agreement a thumbs down, it is scheduled to vote Thursday on whether to ask the European Union to delay Brexit by up to three months.
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.
If EU leaders say no to a short extension but yes to a longer extension MPs will then have to vote on the offer of a longer extension.
Westminster is waiting to see whether Cox agrees that "legally binding" changes to the agreement secured last night are enough to ensure the Irish backstop will not be be permanent.
Some British lawmakers had warned their Brexit-backing colleagues that rejecting the deal could lead to Britain's departure being postponed indefinitely, because a delay would give momentum to opponents of withdrawal.
"It complicates the issue, it leaves us with the possibility still of a no-deal Brexit, and uncertainty over politics more generally".