Gauke said. "The challenge is all very well for people to say I wouldn't do this".
Mrs May responded saying the agreement would ensure a "smooth and orderly Brexit".
Asked whether May was confident that the rest of her cabinet backed the negotiating position agreed at Chequers, which is due to be fleshed out in a white paper later this week, he added: "There is no reason to think otherwise".
So far, Raab has been a minister on housing, regional and local government.
May´s Conservative opponents could trigger a confidence vote against her if at least 48 MPs support it, but to actually force her from office 159 MPs would have to vote against her - a figure hardliners may not be able to reach.
But the furor has gained the attention of her allies.
Some Conservative Party lawmakers warned they would not tolerate a betrayal of Brexit.
"I don't think that would be sensible, it would cause an bad lot of uncertainty, nobody would know with whom they were dealing, and so I think she will survive for those reasons", she said.
Stocker said: "Farming and the environment need stability at this stage, and they will be key industry and public interest areas as we go through future changes that will need special consideration rather than fit into the standard mould".
May has faced a backlash over the plan from Brexit hardliners in her Conservative Party who say it gives too many concessions to the European Union, but she has support from moderates and there has been no challenge to her leadership.
Backbencher Andrew Bridgen became the first Tory MP to declare that he has sent a letter of no confidence in Mrs May to the chairman of the backbench 1922 Committee, Sir Graham Brady.
"I hope that Kit Malthouse will now follow Mr Brokenshire's lead and indicate his willingness to be bold and commit himself to confronting the many housing challenges that we face as a nation". But within 48 hours of their publication, Davis had quit, saying May had already given too much away to the European Union, and Johnson followed. He said "the Brexit dream is dying, suffocated by needless self doubt".
Former housing minister Dominic Raab has been named as the new secretary of state for exiting the European Union, following the departure of David Davis from the role. Brexit may sever United Kingdom banks' passporting arrangements, jeopar-dising their ability to operate across Europe and hindering cross-border money transfers, said Nick Voisey, managing director of the LMA, which represents more than 630 organ-isations.
The Sun, Britain's top-selling newspaper, which has long argued for Brexit, said May had made "blunder after blunder".
"But I come back to this point, if people don't like this proposal what is their alternative?"
But others argued that May had adopted the most realistic plan after losing her parliamentary majority in an ill-judged election past year, leaving her reliant on a small Northern Irish party to govern.