Obama offers a case study in the difference between ideological expectations and a governing reality. The dynamic is almost the opposite of what it is with Romney and the GOP: Whereas Romney has trouble persuading his base no matter what he says, Obama persuaded his base far too easily, with just a few rhetorical sprinklings of Shepard Fairey dust. Partly because of who he was (the first African-American nominee, and one with an exotic name and inspirational speaking style), Obama fed the progressive imagination like no candidate in memory. So the warning signs of what came to define his presidency -- centrism and pragmatism -- were missed.

What are we missing about Romney? Of course many candidates (and presidents) have two or more personas. Franklin Roosevelt shifted position so often that his rival Herbert Hoover "called him a chameleon on plaid," Dallek says. Eisenhower ran to the right in 1952, calling for a "rollback" of the Soviets, then upon taking office embraced Truman-style containment and secretly ridiculed the McCarthyite "primitives" even as he pandered to them. John Kennedy was a public hero and private libertine. Nixon was the wise grand strategist for the history books and, behind closed doors, a panicked paranoiac. George H.W. Bush did "a 180 on abortion and voodoo economics," embracing Reaganite views on abortion as well as supply-side theories that he had previously repudiated, says David Greenberg, a historian at Rutgers and the author of Nixon's Shadow. "It was completely expedient."

Romney's defenders say that the issue of what he stands for is exaggerated. "People do in fact grow and change," says Holtz-Eakin. "The most particular example of that is Ronald Reagan. He raised taxes on individual income in California and supported abortion rights -- and became a very different president."

But Reagan had mastered that conservative song sheet. And he led, rather than followed, the party. The dual-personality problem has never played out so publicly as it has with Romney. Dallek agrees: "All politicians, if they're successful, have some element of opportunism and pragmatism. But this seems particularly pronounced .... Partly what makes it so pronounced is the extent to which there is 24-7 media coverage."

The upshot is that a Romney presidency would almost certainly begin in confusion. Newly elected presidents do try to fulfill their campaign promises, but there's not much he could do to end Iran's nuclear program; a trade war with China would be unpopular and self-defeating; and he couldn't tackle the deficit without raising revenue. Which means that he could find himself besieged by critics on both the left and the right.

Still, even skeptics think that Romney could be an effective president if he finds a way through this minefield of muddled self-identification. "Whereas Obama sees himself as a very transformational figure, Romney is not looking for a spot on Mount Rushmore," says Stanley Renshon, a psychoanalyst who recently published Barack Obama and the Politics of Redemption. "He's just looking to do well by the American people."

Dallek, along with other historians, points out that very few presidents follow a set ideological agenda. FDR made up the New Deal as he went along. Kennedy's "New Frontier" played out similarly. Another prominent historian, the late Arthur Schlesinger, liked to tell the story of his recruitment. Shortly after his inauguration, Kennedy called Schlesinger and offered him a job at the White House. "What will I be doing there?" Schlesinger asked JFK. "I don't know," Kennedy responded. "I don't even know what I'll be doing there."

Kennedy also had to repudiate hard-line views that he campaigned on, such as the "missile gap" with the Soviets that didn't really exist. But unless Mitt Romney learns how to tell people now who he really is -- whoever he really is -- he's unlikely to get a chance to prove just how he might govern.