Brussels (CNN) British Prime Minister Theresa May will face EU leaders Wednesday in a critical summit, as European Council President Donald Tusk warned of an increased risk that Britain would crash out of the bloc without a deal.

Talks over the weekend stalled over the thorny issue of the Irish border. The European Union wants the UK to agree a indefinite "backstop" or fallback position that would ensure an open border between Northern Ireland, which will be outside the EU, and the Republic of Ireland, which will remain an EU member state.

A source familiar with the talks told CNN that negotiators had been very close to a draft agreement, but that it was killed in London by May, who wants any backstop to be time-limited.

Now the British leader has less than 48 hours to turn things around, before she addresses a meeting of European leaders on Wednesday evening.

On Tuesday Tusk described the Irish border question as a "Gordian knot" -- a seemingly unsolvable problem that could only be resolved with bold actions.

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