Instead the plan was brutally rejected in Austria in a series of harsh put-downs that caught Downing Street on the hop and subjected Mrs May to newspaper headlines about being “humiliated”.
Particular fire was directed at Olly Robbins, her top Brexit adviser.
Mrs May hired the europhile senior civil servant last year from the Department for Exiting the EU in what was seen as a move by Number 10 to take more control over the Brexit talks from then Secretary of State David Davis.
Mr Robbins, 43, reportedly recently assured the Prime Minister recently that he was successfully selling her Chequers plan – on which he was her key advisor – to EU leaders and that they saw it as a “game-changer”.
The shock of Thursday’s “ambush” of Mrs May in Salzburg was blamed on his alleged misreading of the runes.
Pro-Brexit Tory MP Iain Duncan Smith said there were “question marks” over how the Chequers plan had got so far.
He stopped short of demanding Mr Robbins’ resignation but Downing Street needed to consider why advisers had blundered.
The former Tory leader and ex-Cabinet minister: “This advice has been off from the word go.
“From the word go there have been question marks over why we were pursuing this when it’s quite clear and obvious the EU couldn’t accept it.
“I’m genuinely concerned Chequers was designed by people who were telling her (Theresa May) this was acceptable to the EU and ‘don’t worry we will get there’.
“It’s clearly a matter for Downing Street to seriously look at, to understand and quickly backtrack why it was the Chequers deal got proposed, because apparently it had been discussed with the EU and they accepted it.
“Him (Olly Robbins) and others, the whole team, really need to look at this – why we were on Chequers when Chequers so obviously wasn’t going to cut the mustard.”
Remain campaigner Gina Miller added her voice to the criticism.
She agreed there was “acrimony and frustration” that the EU had not shifted its stance.
But she added: “They have made it very clear where they stand and the UK has been so focused on its own infighting that they actually have not been listening.
“How can she (the Prime Minister) have been so badly advised? It stinks of incompetence, the whole thing, when the moment of reality is only four weeks away.”
Supporters of Mr Robbins, however, hit back, saying he had warned about possible rejection in Salzburg but been ignored by the Prime Minister’s team.