London CNN  — 

At the eleventh hour, Theresa May claims to have made a breakthrough in Brexit negotiations.

During talks with the European Union in Strasbourg late Monday, the UK Prime Minister and Brexit Secretary Stephen Barclay “secured legally binding changes” to “strengthen and improve” the UK’s agreement on withdrawing from Europe, Cabinet Office Minister David Lidington told Parliament in a statement.

Those changes would not affect the terms of the withdrawal, but offer legal assurances to back it up.

European Commission President Jean-Claude Juncker tweeted that the changes provide “meaningful clarifications and legal guarantees.”

“The choice is clear,” he said. “It is this deal, or #Brexit may not happen at all. Let’s bring the UK’s withdrawal to an orderly end. We owe it to history.”

Juncker’s tweet included two letters to EU President Donald Tusk on the withdrawal agreement. Juncker encouraged the EU to “support the efforts of Prime Minister May to ensure an orderly withdrawal of the United Kingdom from the European Union” in 18 days’ time.

The UK Parliament is scheduled to debate and vote on May’s withdrawal agreement Tuesday.

So far, there’s been widespread skepticism that she can win enough votes to push it through – her previous version of the plan lost by a stunning 230 votes in January.

Lidington said that “negotiations are continuing” in Strasbourg and the British government will update Parliament at the “earliest opportunity.”

Referring to the Tuesday vote, Lidington added that Parliament will have a “fundamental choice”: vote for May’s “improved” deal or “plunge this country into political chaos.”

If they do not vote for the deal, the UK will continue to speed toward its March 29 deadline.

Lawmakers will then have to vote on whether the UK leaves the EU without any deal at all – or whether May will have to go back to Brussels to plea for a deadline extension.