The former Work and Pensions Secretary said the collapse in Cabinet discipline had made the Prime Minister's position "very dubious" and she should consider setting out a timetable for her departure by the Summer in order to get her Brexit deal through Parliament.
McVey quit the government in protest at May's Brexit deal.
Esther McVey has said she would run to succeed Theresa May as Tory leader and prime minister if she had enough support. "There are other issues that are very important for the country - but with the present leadership we are starting to look like a one-issue party and that is not good for democracy".
Speaking to BBC's Pienaar's Politics, Ms McVey said that Mrs May's successor "would have to be a Brexiteer and the cabinet would have to be Brexiteer-minded". She needs a dignified departure, so however that works best for her'.
"She's done so much to try and get this through, even though we're not on the same side of the argument, we are Tories".
She added that, if enough people asked her to stand, she would put herself forward in the next leadership contest.
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Tory MP Andrew Bridgen yesterday said: 'I've been approached by whips offering the PM's resignation if I vote for her deal.' But Government sources denied the claim.
McVey told Sky News' Sophy Ridge on Sunday: "I still believe Theresa May's deal is a bad deal", but said: "The choice is between this deal, a bad deal, or no Brexit whatsoever".
"We have to find a compromise and then be ready to move on".
"The only way I think of resolving this Brexit crisis is going to be to vote for the cross-party backbench amendment calling for another referendum and then get it sorted out by that".
Mr Elphicke, a member of the hardline European Research Group, said: 'What I am clear on is that if we are going to support it, there needs to be a change of negotiating team for the future relationship because there's no way to be carrying on with Parliament.
"The idea that people would be happy if we were dragged out of the European Union on the basis of this unsatisfactory deal and everyone would then be quiet and happy is illusory".