They hit out after ministers caved to intense pressure from Jacob Rees-Mogg's 80-strong European Research Group of Brexiteers, accepting four amendments that sought to harden May's approach.
EU affairs ministers will soon have their first chance to discuss the UK's white paper, the UK's policy on its relationship with the EU after Brexit, and how they would tackle key issues, such as trade between the EU and UK.
The Leave-supporting Conservative MP, who was elected after David Cameron stepped down following the Brexit vote, is the latest official to resign over Mrs May's proposals for the United Kingdom to leave the European Union.
The size of the threat should become clear on Monday when lawmakers vote on amendments to legislation on the government's post-Brexit customs regime, with leading eurosceptics set to vote in favor of amendments that May opposes and back their own proposals to toughen up her exit plan.
May's leadership has been precarious since she unveiled her proposed new Brexit negotiating strategy at her Chequers residence and detailed it in a white paper last week.
But the Prime Minister's spokesman said: 'The British public have voted to leave the EU.
Bringing forward the summer recess would reduce the amount of time Tory MPs have to arrange a vote of no confidence in the PM, should they wish to do so.
Prime Minister Theresa May has been accused of ‘running scared’ amid Brexit turmoil
A second forces the government to commit in law not to allow a customs border down the Irish Sea, which could come into conflict with the backstop's demand that Northern Ireland remains aligned with the Republic for customs purposes.
May's decision not to fight the amendments to her Brexit plan (only agreed at Chequers just over a week ago), tabled by hardline eurosceptic Tories, caused her the departure of yet another government member, as defence minister Guto Bebb resigned in protest at the concessions to hardline Brexiteers. She added: "I have always said I'm in this for the long term".
May's decision improving her prospects of making through to the summer break without a leadership challenge.
She supported remain in the UK's 2016 Brexit referendum.
She told MPs: "I would not have gone through all the work that I did to ensure that we reached that agreement only to see it changed in some way through these bills".
One of the amendments practically says that the United Kingdom should not be collecting tariffs for Brussels unless the European Union does the same for Britain, one of the key ideas in May's original Brexit white paper that was created to keep the Irish border invisible. He told MPs that the issue "has got much more hard since becoming politicised" but was "eminently soluble".
The bill is also due to have its third reading on Monday, and it could be in jeopardy if the angry Tory Brexiters join with Labour, the SNP and the Lib Dems, who are expected to vote against it.
Now you can filter spam calls using Google’s Phone app
Whenever I stick around long enough to talk to a rep so I can ask them to stop calling me again, they immediately hang up on me. Google has now updated the support page of the Phone app to notify the changes which will help users filter spam calls .