Efforts to build support for the plan will see MPs invited to attend presentations organised by Chief Whip Julian Smith and Mrs May's chief of staff Gavin Barwell.
She has also met recently with European Union president Donald Tusk and Irish Prime Minister Leo Varadkar, who said he was briefed on the plan.
With the clock ticking towards a March departure date and passions running high, May needs to thrash out a deal with her ministers on a future customs arrangement with the EU.
A briefing circulated among the ERG, although not yet endorsed by it, suggested the government's plan would leave Britain a "vassal state in the EU's legal and regulatory tarpit".
But it remains unclear whether the European Union will accept her negotiating bid on a free trade area for goods. 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.
"But we'll do it in a way that protects drops and enhances our economy for the future".
He criticised May's decision to maintain a "common rule book" with the European Union, mirroring the bloc's rules and regulations, saying it would hand "control of large swathes of our economy to the European Union and is certainly not returning control of our laws".
"From an Irish point of view there is some quite strong language that is positive, mainly that Britain is absolutely committed to what we call the backstop but more importantly they are determined to ensure that the backstop will never be necessary", Coveney said.
Writing in the Daily Telegraph, Longworth accused May of totally misleading the 17.4 million British people who voted leave, "and left it as late as possible to reveal that she remains a stubborn Remainer".
She said there was a "willingness to sit down and talk" about the plans.
Mrs May has consistently tried to go over the head of Commission chief negotiator Michel Barnier and straight to European Union leaders.
Mrs May said she was "very sorry" the activists did not feel able to campaign, before adding: "This is not a betrayal".
But there were signs of a backlash among some lawmakers from May's Conservative Party on Sunday, including the party's most visible anti-EU campaigner outside the cabinet, Jacob Rees-Mogg.
He added: "We need to do worst case scenario planning".
"An egg that is very softly boiled isn't boiled at all".
Tory MP Anne Marie Morris (Newton Abbot) said: "I've gone very carefully through everything and I can not see how what was agreed at Chequers actually does deliver Brexit, to be honest, hard or soft".
Cabinet Brexiteers have already been persuaded to support the plans after a marathon session of talks at Chequers on Friday, but backbench Eurosceptics have expressed grave doubts.
Of more relevance is whether the position will be acceptable, if at all, to Brussels, which has been strongly pushing back against proposals proposed by London so far.
Morecambe and Lunesdale MP David Morris said the package was "realistic" and Brexiteers now had to be "grown up" about it.
A meeting involving the PM and Tory MPs on Monday evening will provide an indication of the strength of feeling in Mrs May's party.
Vicky Ford urged colleagues not to get "hot under the collar" until they had seen the details.
The report says, "We found that if the United Kingdom reverts to WTO most-favored nation import tariffs, the price of a typical weekly grocery shop would go up by £5.50 (totaling £280 [$370] across the year), the price of a family meal for four at a high-street restaurant chain would increase by £9, and a pair of trainers would become £6.75 more expensive". The Sunday Times said seven of the 27 ministers present spoke out against the plan.
"It would amount to the British government tying the hands of British business".
The new position of the government is to be formalised in a white paper next week.
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