The Work and Pensions Secretary said she was confident the Prime Minister will deliver the “Brexit that Britain voted for”.
Ms McVey was asked by the Reform think tank whether she had full confidence in the Chequers plan, to which she replied: “I will say that I have full confidence in the Prime Minister to deliver the Brexit that Britain voted for.”
But she would not give her backing to proposals agreed at Chequers, which Brexiteers have lambasted as being too soft.
Ms McVey and Penny Mordaunt, International Development Secretary, have been put on “resignation watch” by Downing Street after privately raising concerns about the Chequers plan.
The Work and Pensions Secretary’s partner, Conservative MP for Shipley Philip Davies, revealed he had submitted a letter of no confidence in the Prime Minister after losing trust in the Chequers deal.
Mrs May managed to unite her Cabinet behind her proposals at Chequers and claimed to have restored collective responsibility.
But days later former Foreign Secretary Boris Johnson and Brexit Secretary David Davis both resigned in protest.
On Tuesday the Prime Minister thanked Brexiteer Minister, including Ms McVey, who resisted pressure to resign.
A Cabinet source said: “She said she recognises that some of them feel under pressure following Chequers and thanked them for dealing with it.
“The policy is a change from her Brexit speech made at Mansion House, but it is the only way to get Brexit through.”
But even arch-Remoaner and former Prime Minister Tony Blair said Mrs May’s plan betrays Brexiteers.
Speaking on BBC Newsnight, he said her approach to Brexit was a “fallacy” and her current plan would not keep Brexiteers happy.
He said: “The whole fallacy in Theresa May’s approach.
“If she thinks this honours the Brexit mandate, it doesn’t honour what most people who voted for Brexit think and we know that because they’re saying it.”
He accused her plan of handing victory to “elites” and “betraying” the millions of people who voted in 2016.
The former MP continued: “This is the real triumph of the elite, funnily enough.
“If the system kind of says: ‘Look, we voted to leave, leaving is really a pretty bad idea, so let’s do this halfway house, half in half out. Accept the rules, but you leave the political structures.’
“The irony is that the solution where a majority of the population for sure is going to say: ‘We don’t want that’.
“Because people like me will say: ‘Well, this is pointless’.
“And the true Brexiteers will cry betrayal.”