"The DUP remains firmly opposed to the core tenet of the original plan published by Michel Barnier which would see Northern Ireland remain tied to European Union rules and cut adrift from the rest of the United Kingdom post-Brexit".
May will meet EU leaders in Salzburg on Wednesday and Thursday, as she seeks a breakthrough in talks on the Brexit divorce and the future UK-EU trading relationship.
However, Mr Barnier and French President Emmanuel Macron are up against European Council president Donald Tusk, Germany, Belgium and Poland who think there needs to be a "creative" political declaration to be more aspirational to get the deal agreed.
"I think that the alternative to that will be having no deal", she said, in reference to her so-called Chequers plan which had deeply divided different sections of the political divide.
"The EU has been clear that without an agreement on a backstop, there can not be an agreement on the Withdrawal Agreement".
"But this particular compromise doesn't work because it involves a border in the Irish Sea, no matter how invisible it might be, and we have always been clear that we will not allow that to happen".
Leaving the EU in March 2019 without having signed a withdrawal agreement would be "chaotic and damaging" for the United Kingdom, the Exiting the EU Committee said in a report that appeared to challenge the government's claim it is close to reaching a deal.
Mr Varadkar told the Dail parliament in Dublin: "I do not anticipate there will be any change to the EU's position or any change to our negotiating guidelines".
"Therefore the relationship you have with the British government is extremely important to Northern Ireland", she said.
"Do we really think... that if parliament was to say, 'No, go back and get a better one, ' do we really think the European Union is going to give a better deal at that point?" she said.
He called on other MPs to see through Britain's exit rather than risk an impasse in Parliament, or a general election, saying that the United Kingdom has to "take advantage of the opportunities of being outside the European Union".
Who supports it? This is the official policy of the Liberal Democrats and Jeremy Corbyn is coming under increasing pressure to give Labour's blessing to a vote.
He defended the May government's proposed Brexit deal, which has been roundly attacked by his predecessor, Boris Johnson.
The 67-year-old added that talks were in the "home straight" today, although two key issues remained unresolved ahead of October's deadlines - one being the problem surrounding the Irish border. Tusk wrote Tuesday that "unfortunately, a no deal scenario is still quite possible".
Gove said the responsibility was now with Brussels "because we've shown flexibility".
"This means that our relatives struggle to get visas to come to the UK for family celebrations, restaurants can not employ skilled chefs from overseas, our temples can not bring in priests, and we can not bring people in for business, cultural or sporting as well as the thousands of talented professionals like doctors, teachers and engineers", said Gujarati-origin Priti Patel, former UK Cabinet minister and a prominent pro-Brexit campaigner.
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