Over the past six weeks, Barack Obama has suddenly been acting like the Energizer Bunny of foreign policy. He has jetted off to Asia and back, accepted the Nobel Prize, dispatched new troops to Afghanistan—and just last week engaged in last-minute diplomacy on climate change in Copenhagen.

In all of these efforts, Obama enjoys one huge political advantage: The Republicans are in disarray. On domestic issues such as health care or the estate tax, Republicans seem able to unite behind a common strategy (“Just say no”). But on foreign policy, there is no coherent Republican or conservative opposition.

Cheney seems to think he’s Winston Churchill in the late 1930s—the voice in the wilderness, the scorned leader waiting for the nation to turn to him after it finally realizes how severely it is threatened.

Obama is having trouble moving from his rhetoric to concrete policy achievements. But the Republicans are a step behind him, because they can’t yet figure out what to say. The certainty of George W. Bush’s “Vulcans,” his incoming foreign-policy team, has given way to confusion. The Republicans are looking for a new vision.

Consider, for starters, the two contradictory Republican critiques of Obama’s foreign policy. At times over the past year, conservative critics have claimed that the new administration’s policies really aren’t so different from the Bush administration as Obama’s supporters would like to believe. Look at the surge in Afghanistan, they say. Look at Obama’s acknowledgment, in the Nobel Prize speech, of the existence of evil in the world.

And then on other occasions, conservative critics try to portray Obama as an abrupt departure from the past and a proponent of sweeping change. (A couple of months ago, columnist Charles Krauthammer alluded to Obama’s “radical reorientation of U.S. foreign policy.”) These conflicting Republican views of Obama add up to an incoherent message.

So where are Obama’s Republican opponents headed on foreign policy? Over the past year, three different strands of thinking seem to be emerging. Each one has its own historical model and its vision for the future.

Cheney Republicans. Three decades ago, when Dick Cheney was an anonymous White House staffer, the Secret Service codename for him was “Backseat.” No one would call Cheney that anymore.

The former vice president seems determined to exercise his First Amendment rights day after day to the point of (our) exhaustion. He is the continuing, insistent defender of the Bush administration’s policies on interrogation, on Guantanamo, on executive power. This sets Cheney apart from most other leading Republicans, even hawkish ones (recall that John McCain, the party’s 2008 presidential nominee, disagreed strongly with the Bush administration for years on questions of torture and interrogation).

Cheney’s historical model is pretty clear. He seems to think he’s Winston Churchill in the late 1930s—the voice in the wilderness, the scorned leader waiting for the nation to turn to him after it finally realizes how severely it is threatened. Cheney stands ready to fight them on the beaches, whoever they are. Let’s hope it doesn’t happen.

Muscle Republicans. This group includes political leaders such as McCain and Newt Gingrich and columnists like Krauthammer and Robert Kagan—all of whom push for a strong national defense and an active, assertive American role overseas.

They generally accuse the Obama administration of believing in, and accepting, the idea that America is in decline. The Muscle Republicans argue that the United States is stronger, both militarily and economically, than the liberals believe.

Their historical model comes from a different era: the period from 1977 to 1980, when a new Democratic president, Jimmy Carter, was trying to reshape foreign policy after the Vietnam War. Carter may have underestimated the America’s continuing strengths and certainly misjudged the nation’s mood, thus opening the way for Ronald Reagan’s rise to power. The Muscle Republicans would like to portray Obama as a new Jimmy Carter.

But this critique raises all sorts of questions, both political and intellectual. To accuse your opponents of believing in decline raises the underlying question—well, is there any underlying reality to the idea of decline? Does America in fact have less leverage in dealing with other countries, at least in economic terms, than it had a decade ago, and how much does this matter?

Politically, the Muscle Republicans are in a trap. If the American economy improves substantially before the next presidential election, Obama is likely to win a second term. But if the economy remains weak, and U.S. troops are still fighting in (or have just returned home from) Afghanistan, then it seems doubtful the American public will be attracted to the Muscle Republicans’ message that we should be spending more money on more assertive missions overseas. This is where the Carter-to-Reagan analogy breaks down: At the time of the 1980 election, American troops had already been out of Vietnam for seven years. In 2012, U.S. forces will probably still be in Afghanistan, and Americans will likely be asking when the troops can come home. It doesn’t seem like a propitious time for the message of the Muscle Republicans.

Retrenchment Republicans. One can detect another Republican critique from the opposite direction. It shows up in different ways in the columns of George Will, or the work of the libertarian Cato Institute and of the libertarians’ 2008 presidential candidate Ron Paul. The Retrenchment Republicans argue that the United States should withdraw from Afghanistan and that, more generally, America is overextended and over-committed throughout the world. (A few days ago, in calling for withdrawal from Afghanistan, Paul said, “We cannot afford to maintain this empire.”) If there is a historical model here, it is probably Senator Robert Taft, the leader of the isolationist wing of the Republican Party who lost out to Dwight Eisenhower for the 1952 presidential nomination.

On some issues, such as Afghanistan, the Retrenchment Republicans sound like the left wing of the Democratic Party. But of course, they disagree with the Democratic left on other foreign-policy issues, such as trade, and on virtually all domestic issues.

Right now, the Muscle Republicans are the dominant force among the party’s elites. Their voice is the one you hear from Washington’s conservative-leaning think tanks (other than Cato). Their opinions are reflected day after day on The Wall Street Journal’s op-ed page.

Yet the Retrenchment Republicans could well have strong populist appeal in the Republican primaries scarcely more than two years from now in a country weary of nearly a decade of wars in Iraq and Afghanistan. Republican presidential candidates will have to decide which way to lean, toward muscular foreign policy or retrenchment.

The Republicans want to find a way to attack Obama—but, amid their uncertainty in the post-Bush era, they just don’t yet know from which direction.

James Mann is the author of Rise of the Vulcans: The History of Bush’s War Cabinet, and, most recently, The Rebellion of Ronald Reagan. He is author-in-residence at Johns Hopkins School of Advanced International Studies.