On Monday (14 January), when the date for the long talked about speech was finally fixed, the Conservative leader disappointed some in his party by rejecting calls for a quick referendum on leaving the bloc. But he did seem to offer the public the prospect of a vote after renegotiating London's terms of membership.
In what could be one of the most fateful speeches on Europe by a British leader since World War Two, Cameron is expected to say the euro crisis and the closer integration it is driving is a chance for Britain, which has rejected the single currency, to establish a more arms-length relationship with its 26 partners.
Critics say his manoeuvring risks setting in chain an unpredictable sequence of events that could see Britain quit the Union - willingly or unwillingly - and leave the world's sixth largest economy looking like an offshore version of Switzerland or Norway, with considerably less influence than it now wields.
But Cameron, leading a party and a country with a strong anti-European streak, dismisses such talk as fear-mongering. He says he wants Britain to remain in a reformed EU but to seize back control of areas of public life where he and others believe Brussels' influence has become overbearing and pernicious.
In his speech, Cameron is likely to identify major policy areas - from immigration to employment law and legal affairs - where he wants to claw back core competencies from the EU.
"Right now I think there are a lot of people who say 'I would like to be in Europe, but I'm not happy with every aspect of the relationship, so I want it changed'. That is my view," he told the BBC in an interview on Monday.
With anti-EU feeling on the rise at home, he is likely to promise a rare referendum on any new settlement he manages to broker, part of a process that risks upsetting many countries in the EU, by far Britain's biggest trading partner.
"It would be an act of mutual weakness for the UK and for Europe if Britain were to leave the Union," French European Commissioner Michel Barnier said on Monday.
That message was reinforced by a French diplomatic source in the office of President François Hollande who said Britain could not have an "a la carte" Europe: "Britain cannot be like Norway in terms of its obligations and still benefit from the single market," the source said.
JoaquÍn Almunia, the vice president of the European Commission, said a British decision to leave the EU would be "very bad" for other member states and "a disaster" for London, and he thought it would be "extremely difficult" for Cameron to renegotiate ties with the bloc.
"When you belong to a club you cannot be an influential member saying I don't want to accept this provision," he told the BBC's Hardtalk program.
Cameron on a tight spot
Britain joined the bloc in 1973.
Cameron is in a tight spot. Opinion polls have consistently shown that a slim majority of the British public wants to leave the EU and a powerful clique inside his own party is pressuring him to call an "in or out" referendum.
He is also in danger of being outflanked on the issue by an upstart political party whose popularity has surged.
Yet prominent business leaders, the opposition Labour party, and figures like former Labour prime minister Tony Blair have warned that his stance risks damaging inward investment and damaging Britain's standing on the world stage.
The issue is potentially career-ending for Cameron. Margaret Thatcher, one of his predecessors, was ousted by her party over the EU and it is a subject that has triggered bitter infighting.
The United States, a close ally, is watching closely. A senior US official made an unusually forceful diplomatic intervention into what is an emotive domestic debate last week, saying Washington wanted Britain to stay inside the EU and remain a "strong voice".
That appeared to be a calculated message sent at a time when Cameron was putting the finishing touches to his Europe speech.
Anti-EU rhetoric to deepen coalition rift
Many Britons blame the EU for what they regard as excessive immigration and say they want Britain to seize back full control of its borders and for British judges to not be subordinate to supranational bodies such as the European Court of Justice.
But many others in the EU are growing exasperated by what they see as Britain's new doubts about the European project.
An ally of German Chancellor Angela Merkel warned on 10 January that Cameron risked isolating Britain and paralysing European integration if he held a referendum, while Irish Prime Minister Enda Kenny has described the idea of Britain quitting the EU as "disastrous".
Complicating matters is the pro-EU stance of Cameron's coalition partners in the two-party government, the centre-left Liberal Democrats.
Their leader Nick Clegg has described talk of repatriating powers from Brussels as a "false promise wrapped in a Union Jack" and strong anti-EU rhetoric in Cameron's speech could deepen rifts in the coalition.
Liberal Democrat foreign policy spokesman Martin Horwood said flirting with an EU exit would be taking an "insane risk" with the British economy.
"There are alarm bells ringing in governments around the world that Britain is on some path to exit and that David Cameron hasn't stood up to the Euroskeptics, or Europhobes, in his own party," he told Reuters.
However, anything less than offering a vote containing an option to quit the EU would anger many Conservative lawmakers.
"He could unite 95% of the Conservative Party if he were to announce a renegotiation of the terms of our relationship with Europe followed by an in-out referendum," said Peter Bone, a Conservative Euroskeptic lawmaker.
Any member state has the right to secede from the European Union, though none has ever done so.
Cameron says he is acutely aware of the economic benefits of trading with a single market of 500 million Europeans. The bloc accounts for around half of Britain's trade.
Opposition leader Ed Miliband, whose Labour Party has a 12-point opinion poll lead over the Conservatives, said on Sunday (13 January) it would be "incredibly dangerous" to commit to a referendum on Britain's EU membership: "The prime minister," he said, "Is sleep-walking us towards the exit door."
