May gained some respite when a key Brexiteer in the Cabinet, Environment Secretary Michael Gove, decided to stay - although reportedly to try to influence events in a hard-line direction. Another important Cabinet figure, Home Secretary Sajid Javid, sat on the front bench supporting May in the House of Commons on Friday.
Since May stumbled badly in last year's election, losing her party's majority, commentators have been predicting her demise. Her most dangerous moment, before now, was when then-Brexit Secretary David Davis and Foreign Secretary Boris Johnson resigned in July.
A combination of no obvious successor and fear of a no-confidence vote leading to an unwanted election have helped prop her up.
May has about three weeks to survive and gain support for her plan before Parliament is due to vote on it. There will also be European summits on November 25 and December 13 to navigate.
Initial polling shows the May plan is unpopular in the UK. A YouGov poll had 42 per cent against it and 19 per cent in support. Separately, 44 per cent said they believed a better Brexit deal was possible.
A Skydata poll had May's plan running third with 14 per cent, behind no Brexit at all (54 per cent) and no EU deal (32 per cent) as favoured outcomes.
Skydata also asked people if they would support or oppose a referendum choosing between the May deal, a no-deal Brexit or staying in the EU. The 55 per cent who supported that idea, well outnumbered the 35 per cent opposed.
As the push for a "people's vote" has gained steam, May has tactically begun to hint that maybe no Brexit is a possibility. "We can choose to leave with no deal, we can risk no Brexit at all, or we can choose to unite and support the best deal that can be negotiated."
As she prepares for a difficult week, May is highlighting the stakes of the parliamentary vote and reminding both sides that achieving some of what they want is better than nothing at all.