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."
This story is from the {{IssueName}} edition of {{MagazineName}}.
Start your 7-day Magzter GOLD free trial to access thousands of curated premium stories, and 9,000+ magazines and newspapers.
Already a subscriber ? Sign In
This story is from the {{IssueName}} edition of {{MagazineName}}.
Start your 7-day Magzter GOLD free trial to access thousands of curated premium stories, and 9,000+ magazines and newspapers.
Already a subscriber? Sign In
Happy United back in the goal routine
RASH AT THE DOUBLE AS AMORIM MAGIC RUBS OFF
Horror show for hapless Hamilton
PENALTIES PUNCTURE LEWIS' BID
THREE CARSE IN-ONE
Stokes hails triple threat of England's matchwinner
Reed all about it as Sale roar back
ARRON REED was tipped for \"world-class\" status after scoring two tries as Sale hit Leicester for six.
MOUTH ALMIGHTY!
Lossie cut to 6-4 for Champion
Frasers faces possibility of demotion from the FTSE 100
MIKE Ashley's Frasers Group faces a crucial week with an investors' update on Thursday and potential relegation from the FTSE 100 next Monday.
'I knew when I had the call that she was going to die'
Hell of poison victim’s mum
Putin £100bn war chest vow in bid to finally crush Ukraine
VLADIMIR Putin has approved record military spending for next year as Moscow increases pressure on Ukraine to give up territory in the east of the country.
M Fury as Gregg Wallace hits out at 'handful of middle-class women' who complained about him
MASTERCHEF star Gregg Wallace prompted a backlash yesterday by saying complaints made against him came from a \"handful of middle-class women of a certain age\".
Balmy days are over as winter freeze bites back
THE big freeze will return this week, bringing snow and heavy frost to the north and temperatures as low as -7C.