"In the event of this vote on Tuesday not going through, nobody knows what would happen".
Mr Barnier's latest intervention came after Mrs May delivered a speech on Friday imploring European Union leaders for "one last push" to help her get her deal over the line in the Commons.
The Foreign Secretary said if the Commons crushes the deal a second time, Britain could be forced into a permanent customs union with Brussels - meaning no new trade deals. "That is disappointing. We are within a few days of the next meaningful vote".
Writing in the Sunday Express, Mr Rees-Mogg said: 'The Withdrawal Agreement is a rotten accord. "But we are focused on trying to win this vote on Tuesday".
It was the first time that May had turned directly to the European Union, showing signs of frustration that talks to secure changes to the backstop this week had as yet produced no breakthrough. Barnier told ambassadors on Friday the blame game had started, according to a person familiar with the situation.
There had been speculation the Prime Minister could fly out to Brussels early on Monday to clinch a deal if an agreement on the backstop - meant to prevent the return of a hard border on the island of Ireland - was within grasp.
But despite the war of words, both sides say talks are continuing over the weekend, just days before May will face parliament once again after resoundingly losing the first vote in parliament on January 15.
Jeremy Corbyn, leader of the main opposition Labour Party, said the appeal was "more like a sign of desperation". "We're in very perilous waters". A no-deal Brexit will be "a big problem" for Ireland, France, Poland and Germany, she added.
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Theresa May's hopes of a Brexit breakthrough are hanging in the balance after the European Union appeared to rebuff her latest appeal for help in getting her withdrawal deal through Parliament. To get it approved by March 29, the day set for Brexit, May needs to persuade 116 of them to change their minds - a tough task.
In an interview with the Financial Times, he urged Tory MPs to back the Withdrawal Agreement anyway, saying it would enable him to start spending the "insurance fund" built up in case of a no-deal break.
"But when he courts the Brexiteers, he gives them a very clear narrative that he is only person who can deliver Brexit because of his reach across the party".
"I completely understand uncertainty is really bad for businesses", she said.
"I think it would be very hard for the prime minister to stay in office very much longer".
Leadsom said the United Kingdom economy remains successful and still offers a strong investment opportunity.
He said there would be "plenty of opportunities" to do so in the coming weeks and that Tuesday should be about defeating Mrs May's deal which has already been resoundingly rejected once by MPs by a 230 majority.