"Order!" to keep irritable MPs in line has been particularly critical of the government's decision to postpone a historic vote on the deal expected this week, calling the decision "deeply discourteous".
"Without the ability to genuinely reassure my colleagues that they could not legally be kept in the backstop against their will, it will be hard to get this through the House of Commons".
With the "payroll vote" of ministers, parliamentary aides and trade envoys all likely to have backed Mrs May, a majority of the remaining 160-170 backbenchers voted no confidence in her, said the Eurosceptic and Brexiteer.
Mr Rees-Mogg said that it is time for the "men in grey suits" in the Cabinet - a reference to the ousting of Margaret Thatcher - to tell the Prime Minister to go.
"Are there other ways of achieving the actual backstop itself?" Brexiters in the government and on the backbenches always claim to regard a sovereign House of Commons as a fundamental pillar of leaving the EU.
"If we can't get changes to the backstop that may not be possible".
He told the BBC: "I think the Labour Party, the Labour leadership, is facing a bit of a dilemma".
"This will not happen - everyone needs to know the withdrawal agreement will not be reopened".
"The only people that the Tory party and the Government don't fear is the opposition front bench, because they are not laying a glove on them".
They unveiled a new three-pronged attack to try to force through a second referendum - urging the United Kingdom and European Union to start preparing for the ballot and calling for Jeremy Corbyn to table a vote of no confidence in Mrs May's government.
"Constitutionally, if a Prime Minister can not get their business through the House of Commons, and on Monday the Prime Minister stood up and said she was going to lose so heavily that she wasn't even going to present the vote, and then discovers that the overwhelming majority of her party backbenchers and her non-paid backers have voted against her". I made a promise in the election to call a referendum and I called the referendum.
"In accordance with the rules, a ballot will be held between 1800 and 2000 on Wednesday, 12th December, in committee room 14 of the House of Commons".
Britain's Prime Minister Theresa May tours the Royal Welsh Winter Fair at the Royal Welsh Showground in Builth Wells, Wales, Britain November 27, 2018.
And she took aim at Mr Corbyn, who has resisted growing demands from his own Ms to throw his support fully behind another referendum.