The stakes could hardly be higher as the clock ticks down to the moment the world’s fifth-biggest economy splits from it main trading partner on March 29.
May and the other 27 EU leaders agreed on a draft in November designed to keep the process as orderly and undamaging as possible.
It took nearly two years to negotiate and has managed to upset just about everyone in British politics.
May survived her party’s resulting no-confidence motion but was forced to abort a December vote on the pact after admitting it would lose by a “significant margin”.
There are few signs that much has changed since.
May returned empty handed from a subsequent EU summit she had hoped could address the concerns of her disgruntled Northern Irish coalition partners.
– Vote to go ahead –
Brexit-backing MPs in her Conservative party are still in revolt while opposition Labour leaders are angling for new elections.
May insisted on Sunday that the vote will go ahead as planned on or around January 15. The formal debate kicks off in parliament Wednesday.
But she also warned the deal’s defeat would put Britain “in unchartered territory (in which) I don’t think anybody can say exactly what will happen”.
London has been swirling with rumours about how exactly May intends to avoid Britain crashing out of the bloc without any trade or other arrangements in place.
One idea mentioned by advisers involves the government simply re-introducing more or less the same version of the draft over and over again.
“If we have to have the vote 30 times, we will,” a Downing Street source told BuzzFeed News.
May refused to rule out the possibility of a second or third vote in parliament when pressed about it in a BBC interview Sunday.
Other reports said she intends to invite her party’s most vocal opponents over for private drinks on Monday and Wednesday.
The arm twisting will be accompanied by a new government campaign designed to prepare Britons for the full impact of a disruptive no-deal scenario.
One test on Monday will see up to 150 trucks sent down a highway to the Channel port of Dover to determine how the authorities deal with gridlock.
Dover handles most of Britain’s trade with Europe and is expected to get quickly plugged up if no customs arrangements are made.
But Conservative MP Jacob Rees-Mogg said reports that he and other EU sceptics could be persuaded by May’s arguments about a calamitous no-deal Brexit were “wishful thinking”.
Most Conservatives either “think that these fears are exaggerated or that (it) is a price worth paying for leaving the shackles of the European Union,” he wrote in the Sunday Express.
– Involving parliament –
May outlined a formal plan of action Sunday that included the possibility of giving parliament a bigger say in a new round of trade talks with Brussels that begins once Brexit enters into force.
These “future relationship” negotiations will also try to resolve the prickly issue of keeping the Irish border open while preserving the integrity of the EU.
The temporary solution laid out in the draft withdrawal agreement does not suit Northern Ireland’s tiny Democratic Unionist Party (DUP) that props up May’s government.
“There’s a number of ways which we’re looking to see how we can involve parliament in a greater way in the future,” May told the BBC.
She also promised to continue to seek “further assurances from the European Union” about the border issue ahead of next week’s vote.
The DUP wants a binding guarantee from Brussels that Northern Ireland’s trade with the rest of Britain will not be subjected to any types of checks.
May spent part of her holidays ringing up EU leaders about possible concessions. Brussels has made clear it will cede nothing before the vote.