Cameron appeared to rule out such a vote on Friday - at least for now - telling voters after an EU summit it would not be "the right thing to do", but on Sunday he said the words "Europe" and "referendum" could go together.
Struggling to clarify his position on Monday, he found himself booed by the opposition Labour party in parliament, under pressure from right-wing rebels in his own Conservative party, and at odds with his Liberal Democrat coalition partners.
"Just as I believe that it would be wrong to have an immediate in-out referendum, so it would be also be wrong to rule out any type of referendum for the future," said Cameron.
"Far from ruling out a referendum for the future, as a fresh deal in Europe becomes clear, we should consider how best to get the fresh consent of the British people."
Labour opposition leader Ed Miliband went on the attack.
"Three days, three positions, first it was no, then it was yes, then it was maybe," he said.
As the debt-strapped eurozone eyes greater fiscal, banking and possibly even political integration, Cameron is under growing pressure from the rebellious right wing of his own party to give Britons a vote on whether they wish to remain inside the EU or to downgrade their relationship with Brussels.
London's place in the 27-nation bloc's common market would be at stake in such a vote as - potentially - would London's status as a regional financial hub.
Britain's relationship with the EU has been a toxic issue for the Conservative party in the past, helping topple previous party leaders, and is a headache for Cameron, who has made a string of policy U-turns in recent weeks that have emboldened eurosceptics in his own party to press their demands.
Increasingly restless Conservative party
"Life outside the EU holds no terror .... The people of this country are unhappy with the relationship. It's the duty of politicians to listen," prominent Conservative backbencher and former defence minister Liam Fox told an audience in London on Monday, cranking up the pressure on Cameron.
For many in Cameron's centre-right Conservative Party, which heads the coalition government, the EU is little more than a talking shop and a source of legal meddling that impinges on Britain's sovereignty and holds its economy back.
A string of EU summits that have done relatively little to help solve the eurozone debt crisis has hardened that view, adding urgency to the debate.
"He has a difficult challenge. The Conservative Party is increasingly restless on Europe, because the eurozone is integrating further .... The question keeps returning - he can't deflect it," said Mats Persson, Open Europe think tank director.
If he is to mollify his party's restive backbenches while not upsetting his pro-Europe Liberal Democrat coalition partners, Cameron must tread carefully.
Vince Cable, a prominent Liberal Democrat, has already derided the idea of such a referendum as "horribly irrelevant", reflecting tensions within the coalition whose two partners have increasingly found themselves disagreeing on key issues.
Cameron argues a simple "in-out" referendum soon would not be in Britain's best interests given that Europe's debt crisis may trigger dramatic change in the region, and that Britain might be at a political and economic disadvantage outside the EU.
However, with the success in May local elections of the anti-EU UK Independence Party, and the Labour opposition party also floating the idea of a referendum, the Conservatives risk being outflanked on Europe ahead of a 2015 general election.
That has sowed disquiet among the party's backbenches. More than a quarter of Cameron's party defied him last year when they voted in favour of a motion calling for an EU referendum.
"They are very fed up and they are very worried," said Tim Knox of right-wing think tank Centre for Policy Studies.
Conservative lawmaker John Baron, who last week distributed a letter signed by almost 100 backbenchers calling for legislation for a referendum after planned 2015 polls, said Cameron needed to recognise the public mood.
"Politicians risk losing sight of the fact that people are growing increasingly frustrated that they are not being given a say on the matter," he told Reuters.
