Top EU officials were warned Wednesday to make plans to cope with the fallout from a "no-deal" Brexit as their chief negotiator said talks with Britain must make more progress before next week's crunch summit.
If the budget failed to pass in the Commons, it would be a humiliating defeat for the Mrs May leaving her position all but untenable.
Commenting on the Irish backstop, Barnier said the EU's plan to keep Northern Ireland in the Single Market and customs union would help keep the border invisible - a goal of both sets of negotiators.
He said there would have to be checks on goods travelling to Northern Ireland from the rest of the United Kingdom, because they would effectively be arriving in the EU's single market if there was no hard border with the Republic of Ireland.
He added: "If they (the government) decide to cave in to the unreasonable and unnecessary demands which are being promoted by Brussels, then we will have to consider whether or not they have kept their side of the bargain".
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Rutte said meanwhile that he was "cautiously optimistic" about a deal at the summit.
Labour leader Jeremy Corbyn has said the party will vote against any deal that does not meet its tests, which include retaining "the exact same" benefits Britain now has within the EU's customs union and single market - something the Chequers plan does not fulfil.
There have been warnings that a so-called "hard border" will damage businesses and undermine peace in Northern Ireland.
Just six months before Britain is due to leave the European Union, the two sides differ on their view of the talks - the bloc says a withdrawal deal is within reach, while British officials say "big issues" still lie in the way of any agreement.
"I understand why such procedures are politically sensitive", he said, but added "Brexit was not our choice, it is the choice of the UK".
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The DUP has 10 MPs, although Ian Paisley will not be able to vote in the Commons until November 20 after being suspended for failing to declare two family holidays paid for by the Sri Lankan government.
DUP leader Arlene Foster said that any border effectively being drawn in the Irish Sea between Northern Ireland and Britain would be "catastrophic".
It's looking increasingly likely that if May is going to get a Brexit deal through Parliament, she will have to do so without the support of 9 DUP MPs.
They "will not tolerate a half-in, half-out Brexit" he said, amid reports Mrs May will break the deadlock over the Irish border by keeping the EU's present customs arrangements beyond the transition period in December 2020.
The 27 European Union states will get an update on the negotiations at a meeting of national ambassadors, without Britain, on Friday evening.
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Mr Trump was accused during the 2016 presidential race of sexual misconduct with numerous women. "Hey, @DonaldJTrumpJr. I don't remember, " per CNN ". 'How many years ago was it?' I don't know. "What neighborhood was it in?" I don't know.