There could be three Brexit votes happening this week, depending on the results.
Here are the scenarios that might, in theory, play out in the coming days. If the backstop comes into force and talks on the future relationship break down, May said the unilateral declaration would make clear there was nothing to stop London from moving to leave the backstop.
Juncker believed "it is high time to complete the withdrawal process in line with the wishes expressed by the government of the United Kingdom and to move on as swiftly as possible to the negotiation of our future partnership".
While much of this will, inevitably, come down to a war of words and whether small gestures can change the perception of key voters in the Commons, Theresa May has already been dealt a blow by her own Attorney General, Geoffery Cox, this morning, who wrote in a letter to her that "The legal risk" to having the backstop "remains unchanged".
Following last-ditch talks in Strasbourg ahead of a crunch Commons vote on Tuesday, May said she has now delivered what parliament asked her to do. The main party rivaling May's has now set its sights on a fresh referendum.
"The choice is clear: it is this deal, or Brexit may not happen at all", Juncker said. The U.K. would enter a transition period that would last through the end of 2020.
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The "cliff edge" of a no-deal Brexit was taken off the table with MPs voting 321 to 278 in favour of the motion.
Conservative MP Dominic Grieve remained critical, however, saying that he would not back May's deal.
European Parliament Brexit coordinator Guy Verhofstadt tweeted: "Brexit was about taking back control".
One on Wednesday would decide whether Britain should simply leave on March 29 without any deal at all.
The U.K. and the European Union have agreed to "legally binding changes" to the European Union withdrawal agreement and the political declaration, British Prime Minister Theresa May said Monday night.
This is where, believe it or not, things get even more complicated.
"The further agreement yesterday provided additional clarity, reassurance and guarantees sought by some to eliminate doubt or fears, however unreal, that the goal was to trap the United Kingdom indefinitely in the backstop", Varadkar said.
Mrs May began her day by huddling with top team members in preparation for her final attempt in parliament to sway sceptical MP's hearts and minds. But what would be the point? "However, the matter of law affecting withdrawal can only inform what is essentially a political decision that each of us must make". They wanted a time limit put on the backstop or an amendment that would allow the U.K.to unilaterally revoke it. If that is defeated - the likely outcome - lawmakers will vote Thursday on whether to delay Brexit, something that needs to be approved by the European Union nations too. There could be a renegotiation with Europe, that could mean a second referendum, that could mean a vote of "no confidence" in the Commons against the government.