An alliance of the Labour opposition, hardline Conservative Brexiteers and Northern Ireland's Tory-aligned Democratic Unionist Party could easily keep May from securing the 320 votes she needs before the deal goes to the European Parliament for ultimate assent.
In fact, May's best hope may be that, after the deal goes down initially, the ensuing panic in the financial markets and elsewhere prompts a rethink by enough hardliners or Labour moderates to somehow get it through on a second go around. Her best hope is the least bad outcome, not often a winning hand.
Tony Blair may be persona non grata among Labour these days but he hasn't lost his knack for the sound bite. The way it stands, he says, Britain faces a choice between a painful deal (no deal) and a pointless one.
On the latter point, Blair finds unlikely allies among Brexit's foremost champions like Nigel Farage who argue May's compromise "give[s] away more sovereignty even than as members of the European Union".
But perhaps May's resilience should not be underestimated. I chatted with a retired electrician who thought Brits may rally around the PM if she's seen to be standing up to intransigent Brexit bullies, as well as hardline Remainers, inside and outside her party.
Another factor that comes up everywhere is the shameful irrelevance of Jeremy Corbyn's Labour. Given the state of the Tory Party — torn apart at the seams over this issue — Corbyn ought to be coasting to victory at the next election.
The normal rules of political gravity would have Labour up by 20 points, instead, most polls show them trailing this utter shambles of a government by a few points.
Even among life-long Labour voters I spoke to, there was deep frustration at Corbyn's unwillingness to offer a clear alternative such as a second referendum that may allow the UK to withdraw from the precipice.
Corbyn and his ideological allies have long been sceptical, if not nakedly hostile, to the European project. On the far left, not much has changed since socialist firebrand Tony Benn declaimed entry into the European Common Market as "the decapitation of British democracy".
Corbyn, a card-carrying Bennite, hasn't been able to shake the perception he's fundamentally pro-Brexit.
Little else explains why, under his leadership, Labour hasn't staked out a clearer, not to mention more politically advantageous, position.
A tribal Labour loyalist told me he can't imagine voting for anyone else, but rolled his eyes and muttered "communist" at the mention of Corbyn.
Wherever I went, I found frustration and anger over the way political leaders have mishandled Brexit from the start. But perhaps the prevailing reaction was one of exhaustion. That could be what saves Theresa May.
People are so sick and tired of the uncertainty — so exasperated by the endless posturing on all sides — that what Blair rightly calls "pointless" might be better than any of the alternatives.
• Shane Te Pou is a former activist of the New Zealand Labour Party who works in human resources.
