Liz Truss is facing a backlash from Conservative MPs after firing her chancellor and announcing a second U-turn on a major economic policy.
One former minister told the BBC, “we cannot go on like this indefinitely”.
Another Tory MP said the party was in a “state of despair” after the PM’s Downing Street news conference.
Truss supporter Christopher Chope said “time will tell” if she had done enough to secure her position, calling those plotting to remove her “hyenas”.
Sir Christopher said: “We can’t possibly force another prime minister out of office, we’ve just got to calm down and try to give the prime minister our support.”
In an attempt to end turmoil on the financial markets, Ms Truss sacked her chancellor and close ally, Kwasi Kwarteng, replacing him with former foreign secretary Jeremy Hunt. She then reversed a key policy to scrap a planned rise in corporation tax from 19% to 25%.
It is the second major U-turn on September’s mini-budget after Ms Truss cancelled her plan to scrap the top rate of income tax earlier this month.
At a brief news conference in Downing Street on Friday, the PM dismissed calls for her resignation, saying she was determined to see her promises through.
Commenting on the corporation tax U-turn, Sir Christopher added it was “going to be damaging to the prospects for growth” and was “totally inconsistent” with what Ms Truss said during her leadership campaign.
Conservative MP for Coalville, Andrew Bridgen, said he thought there would “be a challenge to Truss in the next few weeks”.
Mr Bridgen, who backed Rishi Sunak to be leader, said: “Dissatisfaction is so high in the parliamentary party.
“Removing Kwasi Kwarteng when he implemented the policies she asked him to do won’t engender loyalty to her.”
Former Conservative leader William Hague meanwhile said her premiership was “hanging by a thread”.