What happens next could open up a dizzying array of consequences that could increase volatility in global financial markets, especially for the British pound, which slid to a 20-month low against the dollar on Monday.
Failure to approve some version of May's deal in coming weeks would put Britain closer to dropping out of the EU in March with no deal, a worst case scenario that most economic commentators, including the Bank of England, say would lead to a savage recession.
But it could also lead to scenarios under which the country remains close to — or even stays in — the EU. May could draft a slightly different version of her deal with the EU and get it through parliament. Or lawmakers could coalesce around another Brexit deal that would see Britain retain very close links to the European single market. There could even be a second referendum on Britain's exit from the EU.
"It is important to keep these scenarios in mind," says said Erik Nelson, currency strategist at Wells Fargo Bank, as the risk to markets from Brexit "perhaps becomes even more acute in the coming days and weeks."
How markets react could itself influence the politics of Brexit by either striking fear of economic chaos in the hearts of British politicians or — in case of an immediate lack of volatility — encouraging them to take risks.
The prospect of financial Armageddon can be a big motivator for lawmakers. In October 2008, U.S. stock markets nosedived almost 10 percent in a day after Congress rejected a $700 billion financial bailout program, known as TARP. Days later, they approved it.
In Europe, Greece's government came to power in 2015 with a declared mission to scrap the country's bailout program and its tough economic measures. Fears that the country was going to have to ditch the euro currency almost led to a run on the banks, eventually leading the government to sign up to another onerous bailout.
Given the passions involved in the Brexit debate, it's unclear how anyone will respond to financial chaos. The pound will likely be at the forefront of market reaction. It is the main indicator for international confidence in the British economy, as opposed to the FTSE 100 stock index, which is full of multinationals that make their money around the world.
The pound took the biggest hit in June 2016, when the country voted to leave the EU. It slid 15-20 percent against other major currencies — an immediate cut to the wealth of the British that stoked inflation by raising the price of imports. The pound could endure a similar drop if Britain crashes out of the EU without a deal. The Bank of England says it could fall toward 1-to-1 with the dollar.
The currency fell a sharp 1.5 percent against the dollar on Monday, to $1.2538, its lowest in 20 months. International markets could also be roiled if investors believe Britain will leave the EU without a deal. European stock markets fell Monday, with the stock index for export-focused Germany sliding 1.7 percent.
Leaving the EU without a deal would, among other things, see tariffs imposed on hundreds of billions of dollars in trade. Britain would drop out of Europe-wide agreements that govern area such as aviation and prescription drugs, threatening to ground flights and disrupt supplies of drugs. That would create huge uncertainties in a country and region that are home to many of the world's biggest multinationals.
The market reaction in coming days will likely depend on how successful May is in reshaping her deal and how British politicians react. That will all give investors clues as to whether a "no-deal" Brexit becomes more or less likely. And that may not be become clear for days, and possibly not until the new year.
Adam Cole, chief currency strategist at RBC Capital Markets thinks that only after May gets concessions from the EU on a new version of her deal might anti-EU lawmakers in May's Conservative Party back her in a vote.
"This is not to suggest that we are predicting the bill, or a variant of it, will pass before year-end but we do think it is closer to a 50/50 call than the 15/85 that markets appear to price in," he said.
See the AP's Brexit coverage at: https://www.apnews.com/Brexit