The backstop is the fallback position that will effectively keep the United Kingdom in the EU customs union if the two sides fail to agree a free trade agreement that supersedes it.
He said Juncker has "informed me that it has been agreed at negotiators' level and agreed in principle at political level, subject to the endorsement of the leaders".
They say the draft divorce deal would leave Britain tied to the bloc's rules without any say in making them.
That wasn't expected. But an European Union official said the Saturday meeting would go ahead no matter what, indicating an expectation that the outstanding obstacles can be overcome.
"If we had a no deal we'd find ourselves having to find a deal very quickly, so why put our countries and people through that when we have a deal on the table?" he asked.
"And that work will start immediately".
May will meet Juncker for afternoon tea on Wednesday as "part of the ongoing negotiation process", her spokesman said.
If they don't, there's a chance European Union leaders could cancel the gathering, which would deal a major blow to May's hopes of concluding the negotiations by the end of November.
May's Brussels trip resulted in the expansion of the political declaration that accompanies the 585-page divorce deal. Officials had warned that if the text wasn't ready by Thursday morning, the summit was at risk.
Raising the stakes, European Union diplomats said they had been told that German Chancellor Angela Merkel was not willing to come on Sunday for any more talks, meaning a text must be ready beforehand. That declaration covers everything from trade and security.
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But the influx is sure to swell already-high home prices and apartment rents and could overwhelm public transportation systems. As word spread in the last few weeks that Crystal City was on the shortlist to land Amazon , housing demand has skyrocketed.
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"I think people will take a careful look over the abyss. and consider whether they think it is in the best interests of the whole country", Work and Pensions Secretary Amber Rudd said.
The Gibraltar issue "looks quite intractable - but nothing in the European Union is ever truly intractable", one diplomat said.
In answer to one caller, May admitted the Brexit negotiations were keeping her up past midnight most nights, but if the deal was passed she would celebrate with her husband, Philip.
Spain's stance is opposed by both London and Belfast, where Irish Foreign Minister Simon Coveney said a deal that took almost two years to negotiate "should not be changed now".
The publication last week of a draft exit treaty sparked the biggest crisis of May's premiership, with two cabinet ministers quitting and dozens of Conservative members of parliament calling on her to step down.
Opposition to the agreement is also building in the House of Commons in London, which will vote on the final Brexit deal, likely early next month.
But Northern Ireland's Democratic Unionist Party - whose 10 lawmakers prop up May's minority government - has begun abstaining on votes in the House of Commons as a sign of their displeasure at the deal.
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