British business and financial leaders are rallying to say that leaving the European Union would risk economic suicide. But many euroskeptics in Cameron's Conservative Party, including senior ministers in his government, will only be satisfied with a British departure.
The "moderates" in Cameron's party seek a privileged position in which Britain maintains all the trading advantages of membership with few of the social and political responsibilities. And the other 26 members of the European Union are unlikely to accept such a special role.
Fresh Start, a group of 100 Tory parliamentarians, last week called for four major changes to the Lisbon Treaty:
-- A veto power for every EU member on financial issues, to protect the London's role as Europe's top finance center.
-- A British opt-out from Europe's labor and social legislation be moved from the European level back to national parliaments.
-- Another opt-out on European policing and criminal justice issues agreements.
-- New written guarantees that EU countries that are not part of the euro zone will not be placed at a disadvantage in the single market.
Cameron sought to find some elusive compromise to satisfy all camps in a policy speech that he was to deliver Friday, until a postponement was forced by the drama of the foreign hostages at risk in Algeria. The advance text of his speech said, "I want the European Union to be a success and I want a relationship between Britain and the EU that keeps us in it."
He warned that the European Union faced three critical challenges: to reform its systems of governance to respond to the eurozone crisis; to maintain its living standards and welfare systems in a much more competitive world; and to convince the European Union's skeptical citizens that EU institutions were relevant and accountable to them.
"If we don't address these challenges, the danger is that Europe will fail and the British people will drift towards the exit," Cameron's prepared remarks stated.
But his speech was almost as important for what he didn't say about the real implications of a British departure. The European Union would become even more unbalanced with Germany increasingly dominant -- which is something the Germans don't want, so they will try fairly hard to keep Britain in.
And without the United Kingdom, the European Union will lose its strongest voice for free trade, free markets and competition which is one key reason why successive U.S. administrations have pressed the case for Britain in Europe. Another is that a Europe without Britain would be far less committed to the Atlantic alliance.
Britain cannot feed itself nor provide its own energy needs (unless it places massive bets on shale gas and nuclear power) and so must export other goods and services to pay for these essential imports.
So where does Britain export them, given relatively high labor and social costs?
Remember Britain exports more to Ireland than to Brazil, Russia, India and China combined.
Britain would need to revolutionize almost overnight its exporting and trading relationships. What new products would it make and sell, if serious international investment stops coming because the country no longer provides a platform to access the giant EU market?
The main services Britain sells are education and finance. The first might continue if straitened financial circumstances allowed it to continue investing in world-class universities. The second will have increasingly difficulty as the eurozone countries insist on locating the EU financial capital inside the zone, probably in Frankfurt.
Some cherish the fantasy of Britain making a living as a heritage theme park would require it to have an open visa program for tourists, particularly the expected new waves from China and India.
But such tourists are in decline in the United Kingdom because of its visa system. The European Union, with its Schengen system of open borders, needs only one visa for the whole of Europe -- so Chinese tour companies offer Europe only, rather than the extra cost of a second U.K. visa.
And Britain would have to make it even tougher because of its free National Health Service and the prospect of poor Chinese, Indians and others coming to get free treatment or to give birth. Britain would probably have to demand proof of medical insurance or require tourists to pre-pay a bond to pay for possible health costs. Or it would have to turn people away from hospital doors.
Cameron faces the worst of all possible worlds. The toxic issue of Europe will hang over the remaining life of his government, over the next election campaign (due in 2015) and the subsequent period in which he would presumably seek to negotiate a new relationship with the European Union before putting it to the British people in a referendum.
Business leaders and the dwindling band of pro-EU conservatives warn Cameron that uncertainty over Britain's future EU role is already scaring away investors. Nick Clegg, the deputy prime minister (leader of the Liberal Democrats, the junior partner in Cameron's coalition) has warned of a "chilling effect" on the British economy.
Does Cameron have a way out, beyond the Yes-No choice over Europe? He hopes to build a consensus around a policy of "Yes, but ..." which may work in Britain but won't go down well in Europe.
What he hasn't yet tried is a positive case, in which he commits Britain to Europe but as a leading member intent on reforming the manifest flaws of the system. If Cameron were quietly to draft a radical program of reform, and then seek like-minded allies in Scandinavia, Holland and Germany to back it, he could yet transform the nature of the debate and of Europe's future.