Brexit supporters say such fears are exaggerated and Britain would thrive in the long term. There is so far no full exit agreement and some rebels in May's Conservative Party have threatened to vote down a deal if she clinches one.
May's "Chequers plan" - named for the prime minister's country retreat where it was hammered out in July - aims to keep the U.K.in the European Union single market for goods, but not services, in order to ensure free trade with the bloc and an open border between the U.K.'s Northern Ireland and European Union member Ireland.
"It is not acceptable to simply reject the other side's proposals without a detailed explanation and counter proposals", May said. He said there are "positive elements" of the plan but ultimately it is viewed as undermining the single market.
'The second option would be a basic free trade agreement for Great Britain that would introduce checks at the Great Britain/EU border. So May was right when she argued in her pre-Salzburg column in Die Welt that to enforce an "external customs border", a border governed and policed by a foreign institution, between different parts of the United Kingdom would be unacceptable and "no other country would accept it".
"I think it is great that the Prime Minister is standing up for Britain at this time".
Former Tory leader Ian Duncan Smith told the BBC's Today Programme that he believed the European Union had "behaved appallingly" and condemned the "rampant use of their language about a member of the European Union and a British PM".
Speaking about the need to work together, May added: "We need to hear from the European Union what the real issues are, and what their alternative is, so we can discuss them and we can make progress".
At a news conference at the conclusion of the summit, Mrs May struck a defiant tone, saying she had always expected negotiating "tactics" to be used during the course of the Brexit process.
"Until we do, we can't make progress".
'In the meantime, we must and will continue the work of preparing ourselves for no deal.
He said: "We contribute a hell of a lot more than say, some of the emerging European countries that come into the EU".
Theresa May has said she will work to ensure there is no hard border in Ireland, even in the event of a no deal Brexit.
He said: "The manner in which they did it yesterday took many of us by surprise".
Davis told Huffington Post there was a "rock-solid" core of party lawmakers who belonged to the European Research Group (ERG), a grouping which wants a sharper break with the EU and were willing to vote down her plans.
"We need serious engagement on resolving the two big problems in the negotiations and we stand ready".