The Conservative leader has called on Gordon Brown to do the "last bold thing left to him" and call a general election.
During prime minister's questions, David Cameron also asked the prime minister why the communities secretary Hazel Blears remains in the cabinet after an article she wrote on the "lamentable" performance of government.
He said that Blears' tone in the article had been "openly mocking" and that the prime minister has "failed to run a united cabinet".
"The government simply can't go on like this," the Tory leader stated. "Why is [Blears] still in the cabinet?"
But Gordon Brown accused Cameron of reducing "everything to personality".
"Once again, he has got nothing to say about the big issues of the day," the prime minister told the House.
"'Compassionate Conservativism' is gone, gone and gone."
The Tory leader replied: "I am sure that sounded just great in the Bunker."
The prime minster has shown "appalling judgement" in the last week, said Cameron pointing to issues such as MPs' expenses and policy towards Ghurkas.
These are signs of a government in "terminal decline", he added.
"If [Brown] is so confident in his arguments, why doesn't he do what Margaret Thatcher and Tony Blair did after four years of a parliament and call a general election?
"Why not do the last bold thing left to him? Call an election."
But the prime minister said that Cameron was "completely isolated" with politics from the "dark ages".
"He is completely out of his depth when it comes to the big issues of the country," Brown retorted.
"Let's talk about the real issues in government. It is taking big decisions in difficult times and he is simply not up to the task."
Nick Clegg also used the exchanges to attack the prime minister's leadership on key issues.
Referring to Brown's speech on education policy this week, the Liberal Democrat leader said it had failed to address the key issues.
The prime minister insisted that standards in schools had improved, adding that "government has invested more".
But Clegg attacked Brown’s failure to listen, saying that "stubbornness isn't leadership. It’s stupidity".
He said that while the government had criminalised young people, Brown's response was to deliver a "vacuous" speech.
"All he really cares about is saving his own skin," Clegg added of the prime minister.
Brown pointed to schemes such as Sure Start which have been implemented by Labour.
The prime minister accepted that "of course we have got more to do", but added that the Lib Dems should support action that has been taken.
Dods Parliamentary Communications Ltd