U.K. Prime Minister Theresa May won the support European leaders for her Brexit plan this weekend, a crucial milestone in Britain's path to leave the EU in March of next year, but faces a far more daunting task in selling that agreement to lawmakers back home.

European leaders were unanimously in support of May's proposed withdraw agreement Sunday, following months of torturous negotiations between London and Brussels that both defined the terms upon which Britain will leave the bloc next year and set out the framework for future trade talks that could take years to finalize. However, despite May's insistence -- echoed by European Commission President Jean-Claude Junker -- that this was the "best and only" offer on the table, the chances of it being ratified in parliament early next month are extremely low, and its failure could trigger either a leadership challenge or the collapse of her coalition government.

"This has been a long and complex negotiation. It has required give and take on both sides. That is the nature of a negotiation," May is expected to tell lawmakers in a statement later Monday. "And I can say to the House (of Commons) with absolute certainty that there is not a better deal available."

"There is a choice which MPs will have to make," she will say, calling for them to back the deal and allow Britain to "move on," text of her statement read. "Or this House can choose to reject this deal and go back to square one. It would open the door to more division and more uncertainty, with all the risks that will entail."

The pound was little-changed from its Friday levels against the U.S. dollar, despite May's breakthrough, and was marked at 1.2841 in early London trading, suggesting investors are taking a cautious approach to the parliamentary debate, which could culminate with a Commons vote on either December 10 or December 12.

Four scenarios for the Bank of England and Brexit. There could well be others but we couldn't fit them all in

— ING Economics (@ING_Economics) November 25, 2018

At present, there seems little chance that May will win the backing of either her Conservative Party colleagues, dozens of whom have publicly indicated they would vote against it. Historic parliamentary rules effectively mean May will need the support of at least 320 lawmakers to push her deal through, meaning either all of her party, which holds 315 seats, would need to vote in favor, while rebels from the opposition Labour party, which holds 257 seats, would need to be brought on board.

If, as expected, the deal fails to pass that threshold, there are several potential outcomes, including a vote of "non-confidence" by the House, which could trigger a fresh national election, a party vote of no-confidence in May, which could trigger either a leadership challenge or May's resignation, or a demand by lawmakers for May to return to the EU and hammer-out a more satisfactory arrangement.

"This is a bad deal for the country. It is the result of a miserable failure of negotiation that leaves us with the worst of all worlds. It gives us less say over our future, and puts jobs and living standards at risk," Opposition leader Jeremy Corbyn said in a statement Sunday. "That is why Labour will oppose this deal in parliament. We will work with others to block a no deal outcome, and ensure that Labour's alternative plan for a sensible deal to bring the country together is on the table."

Given that May as insisted this isn't possible, and the EU has said there's no alternative to the current deal, investors are likely going to have to face either a new Prime Minister or a divisive national election that will be, in effect, a referendum on the 2016 referendum. There is also the possibility of a formal second referendum, with voters asked to approve May's deal, reject Brexit completely or leave the bloc with no bespoke arrangements of any kind.

"Those who think that, by rejecting the deal, they would get a better deal, will be disappointed," Juncker told reporters in Brussels Sunday.

If U.K. lawmakers think otherwise, December will be an extremely volatile month for European investors. 

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