WASHINGTON—On both sides of the Atlantic, conservatives are furiously looking for a new paradigm.

In Britain, it once seemed as if David Cameron, the new prime minister, was that person. In his early 40s, he looked—generationally, emotionally—like a good fit in today’s society. His open mind about gay rights, ecological issues, to some extent immigration despite his occasional harsh rhetoric, as well as his “new age” style reminiscent of Tony Blair’s, pointed to a new conservative. Americans on the right watched him in the expectation that he might be, as was Margaret Thatcher in relation to Ronald Reagan in the late 1970s, a harbinger of things to come.

But many things conspire against Cameron-the-new-paradigm. His lame victory guarantees a period of ideological muddle, and perhaps new elections. That scenario would be unforgiving for an aspiring Mr. Conservative in any context; at a time when clarity and decisiveness are particularly urgent, it yells failure.

Even before the elections Cameron was making many compromises on the issue that should matter most to any conservative today: the urgency of redressing the balance between a government that has grown explosively in the wake of the two-year financial crisis and a society hooked on living beyond its means. The deficits, the nationalizations and the vast amounts of money created by central banks in response to the crisis are but symptoms of that basic imbalance. Cameron’s response is to try to square the circle: He has offered to cut four pounds of spending for every pound of increased taxes, while promising to protect all entitlements and the National Health Service as well as to keep a strong currency.

In a world in which deficits amount to 10 percent of gross domestic product and debt levels are mirroring the size of the economy in developed nations, the new Mr. or Mrs. Conservative needs to make a return to fiscal sanity part of his of her life’s work. In a world in which doubling the monetary base and owning banks and car manufacturers is considered an admissible form of crisis management on the part of the state, he or she needs to make returning to private enterprise a relentless cause.

But there is more. Contemporary conservatism is torn by the pursuit of incompatible goals, something of which Cameron seems unaware. Even Reagan delivered small government on some issues and big government on others because of the intention to use it as a force for good in the world and moral rectitude at home. Thatcher was somewhat more consistent in limiting government, but could not go far enough. A few years after she left office, government amounted to 50 percent of the size of Britain’s economy once again. Subsequent conservatives, with less ideological conviction, fared even worse—hence George W. Bush’s fiscal legacy.

Incompatible goals are compounded by incompatible temperaments. The divisions over social issues among conservatives in the United States spell divisions between more tolerant and less tolerant dispositions. The civil war of sorts tearing the Republicans apart—of which the tea party movement is a symptom—reflects a divide not just over the extent of government intervention in the economy but also over how much power government should exercise in foreign policy and social issues.

Finally, Cameron faces a problem peculiar to contemporary British conservatism: the confrontation over further integration in Europe. It was partly the cause of Thatcher’s fall and the undoing of her successor, John Major. The current troubles in the European Union have undermined the pro-European Tories vis-a-vis the Euroskeptic Tories but the dust is far from settled. Do Euroskeptics truly oppose European integration because they fear statism, or are they just little-Englanders cloaking their naval-gazing instincts with the robes of Euroskepticism? Cameron has yet to respond.

The international race for Mr. or Mrs. Conservative, then, is wide open. Perhaps the answer for conservatives lies in going back to their philosophical roots, whether in the form of Britain’s Edmund Burke or the Founding Fathers of the United States. In 1960, Barry Goldwater—the United States’ Mr. Conservative—wrote that “the ancient and tested truths that guided our Republic through its early days will do equally well for us. The challenge to conservatives today is quite simply to demonstrate the bearing of a proven philosophy on the problems of our time.”

Those aspiring to his mantle ought to bear that in mind.