Speaking shortly after two of May's most senior cabinet ministers resigned over her Brexit plan, May said the models on offer from Brussels were unacceptable.
A concerted effort to win over would-be rebels has been mounted by Downing Street, but Mrs May faces a potentially stormy private meeting with Tory MPs and peers in Parliament on Monday night.
Writing in the Mail on Sunday, he said Jacob Rees-Mogg was now the only credible challenger to Mrs May, after Brexiteer cabinet ministers failed to oppose the PM's plan.
Mr Rees-Mogg refused to support her and said that "she would be well-advised to revisit her Brexit policy".
There had been talk of resignations over the plan, which could keep Britain tied to the bloc for years after Brexit, even if officials stress parliament would reserve the right to diverge.
She will tell MPs it was "the Brexit that is in our national interest" and "will deliver on the democratic decision of the British people". We will end free movement, we will end the jurisdiction of the European Court of Justice, we will stop sending vast sums of money to the European Union every year, we will come out of the Common Agricultural Policy, we will come out of the Common Fisheries Policy.
She seems to have reassured pro-Brexit ministers that under the new negotiating position Britain will still be able to seek trade deals with the rest of the world, easing fears that mirroring European Union rules for goods would rule that out.
But even if there is an agreement at home, May will then have to get the support of the European Union, which poured cold water on her earlier suggestions for customs arrangements.
Instead, they have fostered a deep distrust among many eurosceptics in her party, undermining her position and casting doubt over the Brexit process.
Meanwhile Backbencher Andrea Jenkyns said she was "awaiting the detail" of the plans before deciding whether to support calls for a leadership contest.
It's unclear how European Union negotiators will react to the plan, which seems to fly in the face of European Union warnings that the United Kingdom can not pick and choose which aspects of European Union membership it would like to keep, and it is already angering hard-line Brexiteers who advocate a total break with the EU.
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Turkey's audiovisual authority RTUK later said the government had issued a temporary ban on broadcasting images from the scene. Over the past few years, Turkish cities have been building high-speed rail lines to replace the country's ageing network.
"Obviously if the government and the prime minister continue to support that very poor offer then I won't have any confidence in the government or the prime minister".
The veteran Tory eurosceptic Bill Cash told Sky News: "There are a lot of questions in here, there is a lot of unhappiness, there is a great deal of concern that we are saying that we leave - it's not "to be or not to be", it's "to leave or not to leave". "Time is short. We need to have quickly realistic and workable solutions".
The plan was "the ultimate statement of managing decline" and "focuses on avoiding risk, not on the world of opportunity outside the EU".
James Cleverly, a deputy chairman of the party, said: "I went in there with some concerns as a Brexiteer and I come out with those concerns addressed".
"He told the BBC's Andrew Marr Show: ".I'm a realist and one of the things about politics is you mustn't, you shouldn't make the ideal the enemy of the good.
The 30-strong Cabinet is being sequestered Friday inside the prime minister's Chequers country retreat - without their phones - to discuss a compromise plan that May hopes will unite the government, and be accepted by the bloc.
The Environment Secretary has warned Brussels that ministers have agreed to "step up" no-deal preparations and that if it remains "ungenerous and inflexible" Theresa May will have to "contemplate walking away".
"With her government in chaos, if she clings on, its clear shes more interested in hanging on for her own sake than serving the people of our country", Corbyn said.
Sir Martin Donnelly said that the UK doesn't have the same clout as the European Union when it comes to trade with the United States.
His resignation seemed to spur others to follow suit, with a source saying that a junior minister in the same department had also quit, just two days after May had held a crisis meeting with ministers to overcome the deep divisions over Brexit. We are now pursuing a fragile "least worst" option.