Disgruntled MPs - including one minister - issued open calls for the Prime Minister to assert Tory pre-eminence over Lib Dem coalition partners and ditch "barmy" policies on gay marriage and reform of the House of Lords.
Meanwhile, Ed Miliband said Labour was "winning back people's trust", after outperforming expectations by scooping more than 700 new councillors in England and Wales.
In Labour's best night at the polls since Tony Blair's leadership, Mr Miliband saw his party make inroads into the south of England, seizing key councils such as Southampton, Exeter, Plymouth, Reading and Harlow and even snatching seats in Mr Cameron's own Witney constituency in Oxfordshire.
Speaking to cheering activists in Birmingham, where Labour won back control after eight years of opposition, Mr Miliband said his party had won by showing it was "in touch with people's concerns".
"This Government promised change and they have made things worse, not better," said Mr Miliband. "They are standing up for the rich and powerful, not standing up for the millions of ordinary families who need help. The message of these results is that when you have a Government piling unfairness on top of economic failure, people are not going to support them."
The one blemish on Mr Miliband's day came during a post-election visit to Southampton, where he was hit on the shoulder by an egg.
Liberal Democrats endured a bruising night, shedding 297 councillors to reach their lowest level of local representation since the party was formed in 1988.
Mr Cameron was still hopeful of a silver lining in the shape of victory for Boris Johnson in the London mayoral election, where the Tory incumbent was leading his Labour rival Ken Livingstone in early counting.
But the Prime Minister's enthusiastic call for "a Boris in every city" was dealt a firm rebuff by voters, who rejected the introduction of elected mayors in eight cities. In 11 referendums held around England, only Bristol voted to create an elected mayor and Doncaster to retain theirs.
Lib Dem leader Nick Clegg said he was "really sad" at his party's results, but added: "I am determined that we will continue to play our role in rescuing, repairing and reforming the British economy. It's not an easy job and it can't be done overnight but our duty is to boost jobs and investment and to restore a sense of hope and optimism to our country."
Mr Cameron apologised to Conservative councillors for the loss of their seats, which he blamed on the tough economic backdrop against which the elections were held.
He said: "These are difficult times and there aren't easy answers. What we have to do is take the difficult decisions to deal with the debt, deficit and broken economy that we've inherited and we will go on making those decisions and we've got to do the right thing for our country."
Mr Cameron came under intense pressure to change course from MPs on the right of his party, who fear a haemorrhage of traditional Tory voters to the UK Independence Party unless he refocuses the Government's agenda on mainstream priorities.
"David Cameron, I think, is on notice that he does need to raise his game," former ministerial aide Stewart Jackson, told BBC Radio 4's The World at One.
"He needs to concentrate on bread and butter issues likes jobs and mortgages and public services and above all develop a clear route map to growth and stop fixating on the agenda of a liberal clique and barmy policies such as Lords reform and gay marriage."
Epping Forest MP Eleanor Laing urged the Tory leader to "give rather less regard to the Liberal Democratic intellectual urban elite with the student politics ideas of reforming the constitution and taking forward green policies", while former frontbencher Gary Streeter said his constituents were "gagging" for a tougher line on traditional Tory priorities like law and order.
And defence minister Gerald Howarth also expressed doubts about the Government's agenda, saying: "There are issues, for example, like the proposals for gay marriage. A lot of Conservatives have written to me saying 'I am a lifelong Conservative, there is no mandate for this, why is this being proceeded with?' There is the business of trying to change the House of Lords. Do we need to do this at a time when the nation is preoccupied with restoring the public finances?"
Mr Cameron and Mr Clegg are expected to attempt a relaunch of the coalition next week, with a joint press conference ahead of Wednesday's Queen's Speech, which will set out the Government's agenda for the coming year.
ut Mr Clegg faced a warning from a senior Lib Dem peer that his party may not be able to fight the 2015 as an independent national party unless the Government changes tack on the economy.
Accusing Mr Cameron and the Treasury of "pussyfooting about" on the issue, he called on ministers to force banks - particularly those part-owned by the state, such as RBS - to lend to business.
Lord Oakeshott, a former party Treasury spokesman and close ally of Business Secretary Vince Cable, said: "For me, what matters is whether we can fight the next election as a nationwide, powerful, independent force, and if we have another year like this, we won't be able to."
He warned: "The economy is flat on its back and if we can't get the economy to grow, we can't get the deficit down. So unless there is a change, both coalition partners and our country are heading for the rocks. That is why we have got to take bold action now on the economy."
