Senior MPs argue that Conservative voters did not vote in local elections because they are "deeply angry" with the Government's inability to deliver.
But former leader Sir Iain Duncan Smith says the general election is still up for grabs if the PM and the party fight for it.
Writing in today's Daily Express, he said: "Despite the bad results it is not over yet.
"We must clear the decks and recognise that in the next few months nothing else matters but delivering on the public's priorities.
'The only question that matters is, are we Conservatives up for the fight?"
MPs are calling for reforms including help for those pensioners dragged into paying tax for the first time in retirement, help for the self-employed and introducing drastic curbs on green levies.
The demands come after Labour claimed a series of key victories in the local elections. A Downing Street source said the results were "disappointing" and that it was difficult to lose talented people.
But the insider insisted the vote share achieved by Labour shows Sir Keir Starmer is "yet to seal the deal" and he would have to rely on a rainbow coalition of the SNP, Greens and Lib Dems to get into No10.
The source added: "The PM is up for the fight and is working continuously to keep delivering.' Backbencher Sir Jacob Rees-Mogg said: "It is time to show that we are on the side of the voters rather than the bureaucracy."
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