Then on Wednesday, some of her party's lawmakers sought to oust her. She survived a no-confidence vote, but suffered a serious blow to her authority. May also appears no closer to finding a solution for her country.
Brexit is complex and can seem daunting even to Brits who try to keep up with this stuff. And if the landscape was uncertain before Monday, it's perhaps even more so now.
"I'm just as clueless as everyone else," joked Anand Menon, a professor of European politics and foreign affairs at King's College London. "You might as well talk to the next person you see in the street."
Here are five potential scenarios that could play out in the weeks ahead.
The U.K. currently has a deeply entrenched relationship with the E.U. as one of its 28 member states.
British members of Parliament, or MPs, are currently trying to decide what those links will look like after Britain leaves this club on March 29.
The prime minister has negotiated her own deal with the E.U. but most British lawmakers hate it. It was almost certain to be rejected in a defeat of humiliating proportions — that's why May pulled the vote originally scheduled for Tuesday.
The simplest way to resolve the Brexit conundrum — at least for now — would be if the prime minister found a way to get her deal through the House of Commons.
In its current state, this seems impossible. The parliamentary math is stacked against May, with as many as 100 of her party's 315 lawmakers openly opposing the plan. The enormity of her task was hammered home Wednesday after 117 of these same politicians voted against May in an unsuccessful leadership challenge.
The border is currently more or less invisible and there are no checkpoints.
The riddle is how to create a boundary that checks goods and people crossing the new E.U. border, but avoids risking a return to "The Troubles" — a conflict that for decades blighted Ireland and the U.K. until a peace deal in 1998.
Some fear the reinstatement of a physical boundary could rekindle tensions and even spill over into violence.
In a bid to resolve this, May's plan includes something called the "Irish backstop."
This is an insurance policy that would come into force if the U.K. and E.U. can't agree on a solution to this border issue. It would prevent a hard border by tying Northern Ireland to some of the E.U.'s regulations.
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However, some are concerned that creating one rule for Northern Ireland and another for the rest of the U.K. — England, Scotland and Wales — potentially risks breaking up the country. Scotland voted to remain in the E.U. and its government might ask for a similar arrangement.
Others say the backstop gives the E.U. too much power.
This is why May's deal faces such stiff opposition. She is now returning to Europe to seek "assurances" that this backstop would be never used.
What she hopes to achieve is unclear. E.U. officials say that they will not budge on what they've already offered her, let alone give the type of sweeping changes May would need to convince dozens of lawmakers in her own party to change their position on her proposal.
"I think we're beyond the stage where a little bit of unicorn dust on the political declaration is going to swing it for her," said Menon, who is director of The U.K. in a Changing Europe think tank.
The opposition Labour Party has been deeply critical of the government's efforts. But it has also faced criticism for failing to articulate a coherent alternative.
Labour leader Jeremy Corbyn has remained vague on his position but it's no secret he's a longtime euroskeptic. He has resisted calls to become a leading voice of the anti-Brexit movement, instead maintaining Labour's position that there should be a general election so he can attempt to succeed where May has failed.
His detractors say he has not explained how exactly he would do so.
Gaining power would require persuading a majority of lawmakers to back a no-confidence motion on May's Conservative government.
After chastening losses in a general election last year, May no longer commands an absolute majority in the House of Commons. Instead, she is propped up by the Democratic Unionist Party, a small group from Northern Ireland who have acted as her parliamentary kingmakers.
The Scottish National Party and other smaller groups said they would back a no-confidence motion. But Corbyn would need the Democratic Unionists to turn against the Conservatives, something they've said they won't do. So unless something changes it's hard to see how he can make the arithmetic work.
Either way, a new prime minister or a new government would not be a solution in and of itself: A new leader would still need to solve the Brexit question. If they don't, that would lead to...
Once Britain leaves the E.U., its borders will be subject to all sorts of checks and regulations that it currently doesn't need to worry about. If it crashes out of the bloc without a plan, many are warning it could have truly scary consequences for the British people.
This is the default option: If lawmakers in Parliament do not find another solution, Brexit will still happen on March 29.
A "no-deal" Brexit would be "absolutely catastrophic" for Britain and put the country "in a state of emergency," Conservative lawmaker and former attorney general Dominic Grieve told Sky News this summer. "Basic services that we take for granted might not be available."
As the days tick ominously closer to the March 29 deadline, the prime minister and the Labour Party may both try to use the looming threat of no-deal to persuade lawmakers to back their respective plans.
Whatever happens, lawmakers will most likely do everything possible to avert this. Leading to another potential outcome ...
Hours before the prime minister canceled her Brexit vote on Monday, another pivotal piece of news dropped: The European Court of Justice ruled that Britain can effectively cancel Brexit if it wants to.
The court said the U.K. could do this by withdrawing the divorce clause — called Article 50 — that it triggered in March 2017. Crucially, it wouldn't need to ask the other 27 E.U. member states.
Most British lawmakers don't want to do this, either because they still believe in Brexit, or because they don't want to go against the 2016 referendum decision in which 17.4 million voters backed leaving, compared to 16.1 million who supported the status quo.