Senior Tories have urged Boris Johnson to make changes following a huge by-election defeat for the Conservatives.
Ex-Conservative leader Iain Duncan Smith said No 10 needed discipline while another senior Tory said the PM needed to get "a bit of a bloody grip".
Mr Johnson said he was "disappointed" with his party's performance in the North Shropshire vote.
The Lib Dems who won the ultra-safe Tory seat, said voters were "fed up" with Mr Johnson's "incompetence".
The party's candidate, Helen Morgan, overturned a Tory majority of almost 23,000 at the last general election to win by 5,925 votes, saying: "The people of North Shropshire have spoken on behalf of the British people. They have said loudly and clearly, 'Boris Johnson, the party is over.'"
Their historic victory came after a week dominated by claims of Covid rule-breaking in No 10 and a revolt by Mr Johnson's own MPs over restrictions.
The PM blamed a "constant litany of stuff about politics and politicians" in the media for the result.
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Although few have commented publicly, Conservative MPs are said to be divided over Mr Johnson's future.
Iain Duncan Smith - who led the party for two years - told the BBC the government had lost focus as a result of stories about Downing Street parties.
Iain Duncan Smith says the PM "gets there has been a series of things happening which should not have done”.
He also criticised Conservative MPs calling for a Mr Johnson to be replaced saying "I want my colleagues to stop playing games.... the party has to get behind him."
Veteran backbencher Sir Roger Gale described the result "as a referendum on the prime minister's performance".
And former Scottish Tory leader Baroness Davidson told BBC Radio 4's World at One that Mr Johnson was "drinking in the last-chance saloon".
She said Conservative MPs were "looking for a bit of a bloody grip" and an end to the government's "own goals".
Watch Boris Johnson's reaction to the North Shropshire by-election defeat
Responding to his party's defeat, the prime minister said: "Clearly the vote in North Shropshire is very disappointing result. I totally understand people's frustrations. I hear what the voters are saying."
The defeat comes at the end of a torrid week for Mr Johnson, during which 100 Conservative MPs rebelled over government proposals to introduce Covid passes in England.
There have also been criticisms over Downing Street Christmas parties during restrictions last December.
The prime minister put much of the blame for the by-election defeat on media coverage, saying that "what the people have been hearing is just a constant litany of stuff about politics and politicians and stuff that isn't about them".
"The job of the government is to make people like you [journalists] interested in the booster roll-out and skills and housing and everything else we're doing," he added. "Unfortunately we haven't been able to get the focus on those issues."
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Analysis box by Laura Kuenssberg, political editor
Boris Johnson is in a very precarious position, not just because of the monster by-election defeat in North Shropshire.
This week huge numbers of his own backbenchers didn't back him on a key part of his plans to deal with the pandemic, and there was a report on how the lavish redecoration of his flat above Downing Street was paid for.
There is a difference of opinion inside the Conservative Party of whether or not this is a situation that can be recovered from.
Some MPs think it's a situation past saving and are focusing on when and how a change at the top can be conducted. Others, however, don't believe it's terminal.
Mr Johnson said one of his stock lines - that he takes responsibility for everything that happens in the government. That's not the same self-reflection that some of his colleagues would like from him right now.
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Lib Dem leader Sir Ed Davey, who is isolating with Covid, said his party could now beat the Conservatives "anywhere", adding: " I think people are so fed up with Boris Johnson, so fed up with his incompetence and his behaviour, I think they'll be really happy about that."
The by-election was called because previous North Shropshire MP Owen Paterson quit in November after being found guilty of breaking parliamentary rules on lobbying - trying to influence government policy - in return for money.
Fourteen candidates stood, with Ms Morgan taking 17,957 votes, while Conservative Dr Neil Shastri-Hurst got 12,032 and Labour's Ben Wood came third with 3,686.
Labour, which came second in the constituency at the 2019 election, saw its share of the vote fall from 22.1% to 9.7%.
The North Shropshire result is the second loss of a former Conservative stronghold to the Lib Dems this year, with the party seizing Chesham and Amersham, in Buckinghamshire, in July.
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