London (CNN) If lawmakers don't take their final chance to vote for British Prime Minister Theresa May's Brexit deal on Tuesday, then -- in the words of European Commission president Jean-Claude Juncker -- the United Kingdom might never leave the European Union.

In Strasbourg late last night, Juncker referred to the first defeat of May's plans back in January and warned: "In politics sometimes you get a second chance, it's what you do with the second chance that counts, because there will be no third chance ... it is this deal or Brexit might not happen at all."

Whether rebellious Brexiteer Conservatives believe him is another thing entirely. They have, after all, spent months forcing the Prime Minister to go back and forth to Brussels and Strasbourg to make the changes they demanded.

If they don't, May's position as Prime Minister is in serious danger -- and Britain will inch towards a no-deal Brexit or, at least, face a delay to the entire process.

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Later on Tuesday, May will appeal to lawmakers in the House of Commons to back her deal -- which, she claims, is now enforced with "legally binding" changes designed to assuage concerns about the UK being locked into permanent arrangements with the EU and undermine Brexit.

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