Ms Truss survived a meeting of her Cabinet without being told to quit on Tuesday, but has lost support of her MPs and now the membership.
A snap poll found more than half wanting her to resign, with 83 per cent saying she was doing a bad job.
It came as the Prime Minister dropped a commitment to increase state pensions in line with inflation, a decision that will only make her precarious position worse.
As Tory MPs desperately planned ways to end her premiership and install a unity candidate, Downing Street insisted Ms Truss was focused on the challenges facing the country rather than party infighting.
Asked whether Ms Truss was concerned about ministers discussing replacing her, the Prime Minister’s official spokesman said: “Her view is she needs to be focused on what is right for the country rather than on any internal discussions among the party at the moment.
“She is conscious that these are globally difficult times and the UK is in a difficult situation economically.”
This focus on the country comes despite the Prime Minister now having frequent meetings with MPs to try and win them over, as well as the installation of Jeremy Hunt as Chancellor to shore up support on the left of the party.
Tuesday’s Cabinet meeting was dominated by discussions on spending after the Chancellor tore up Ms Truss’s original plan for tax cuts and increased public borrowing.
Asked if ministers offered their support, the spokesman said: “Certainly ministers were very involved in the discussions around preparations for the medium-term fiscal plan.”
When he was asked if any of the Cabinet suggested Ms Truss should quit, the spokesman said: “No.”
The challenge facing the Prime Minister was underlined by a YouGov survey of 530 Conservative Party members carried out on Monday and Tuesday, which saw 55 per cent say she should resign, and only 38 per cent back her staying on.
About 39 per cent of those who voted for Ms Truss in the Tory leadership race said she should quit, compared with 57 per cent who said she should not.
Some 83 per cent said she was doing badly as Conservative leader, compared with 15 per cent who said she was doing well and 2 per cent saying they were unsure.
Her approval rating is now worse than any leader ever recorded, and things got worse with further polling on Tuesday evening.
A separate YouGov survey found 77 per cent of Britons now disapprove of the UK Government, the highest in 11 years of YouGov tracking data.
MPs are now hoping to appoint a unity candidate, with Boris Johnson the current favourite among members, on 32 per cent, followed by former chancellor Rishi Sunak on 23 per cent.
Some 60 per cent said they would back a proposal of a unity candidate to succeed Ms Truss being chosen without members having a say.
It came as Ms Truss risked a further row with her base, with Downing Street suggesting ministers could ditch their commitment to the triple lock.
Mr Hunt told colleagues at a Cabinet meeting on Tuesday they must find savings from their departmental budgets.
As recently as October 2, Ms Truss was clear state pensions would increase in April by whichever is highest – 2.5 per cent, wages or inflation.
“I’ve committed to the triple lock. Yes,” she said in a BBC interview.
But, after replacing former Chancellor Kwasi Kwarteng in the Treasury after their disastrous mini-budget, Downing Street backed down on this pledge.
The Prime Minister’s official spokesman said: “We are very aware of how many vulnerable pensioners there are and indeed our priority ahead of this fiscal plan is we continue to protect the most vulnerable in society.
“The Prime Minister and the Chancellor are not making any commitments on individual policy areas at this point, but as I say the decisions will be made through the prism of what matters most to the most vulnerable.”
The spokesman did, however, stand by the commitment of increasing defence spending to 3 per cent of GDP by 2030.
Labour’s shadow work and pensions secretary Jonathan Ashworth said: “Tory MPs have already imposed this year the biggest real-terms pension cut ever for Britain’s retirees and their disastrous budget has them considering further cuts to pensioners’ incomes.
“Pensioners deserve so much better than Liz Truss and her disastrous mistakes that are leaving older people paying the price.”
The Liberal Democrats’ pensions spokeswoman Wendy Chamberlain added: “It would be a kick in the teeth for millions of people if Truss now backtracks on her triple lock promise. The British public will never forgive the Conservative Party if they break this promise.”
In the Commons on Monday, Mr Hunt did not rule out the triple lock being suspended as he refused to make any commitments on “individual policy areas”.
Around 12.5 million people who receive the state pension could be dealt a real-terms cut in earnings if their payments do not rise in line with inflation, standing at around 10 per cent.
On Wednesday, the Office for National Statistics will publish the Consumer Price Index measure of inflation, on which changes to benefits and pension payments are calculated.
Earlier, Ms Truss was warned by a senior minister that she cannot afford to make any more mistakes as she battles to stay in No 10.
Armed forces minister James Heappey said: “She’s very much our Prime Minister and, for what it’s worth, I think she’s doing a good job.”
But he told Sky News that “given how skittish our politics are” at the moment, “I don’t think there’s the opportunity to make any more mistakes”.