One goal of the Iraq war's architects was to demonstrate the magnitude of America's capacity to reshape the world.

The war did exactly that, but not in the way that its supporters intended. The overthrow of Saddam Hussein and accelerated construction of an Iraqi democracy was designed to show both the costs of threatening U.S. interests and the benefits of political freedom. Instead, the long struggle has offered a painful lesson in the limits of America's ability to bend the world to its purposes, and even to anticipate the consequences of its actions. As President Obama somberly lowered the curtain with his speech this week declaring the end of combat operations, the experience remains far more humbling than inspiring.

The swift deposing of Saddam dramatized America's military superiority. But the insurgency and disorder that then spiraled out of control in Iraq showed that even such a mighty hammer could not flatten every nail. The troop surge that President Bush ordered, and Gen. David Petraeus executed, brought Iraq back from the abyss of chaos and civil war in 2007. But even that intervention has hardly produced the beacon state that Bush and the war's planners sought to erect on the ashes of Saddam's dictatorship.

Although violence is greatly reduced from Iraq's darkest days, it continues to flare with terrifying effect. And even as Iraq has made progress in building a functioning government, the country remains torn by religious divisions and locked in political stalemate. Across the wide range of political, security, and social indicators, the common verdict may be that Iraq is better off than seemed possible at its lowest point but not nearly as well positioned as the war's supporters anticipated in 2003 (or perhaps even in the most optimistic days after the surge).

The real question should be whether this equivocal result justifies the war's vast cost. The Congressional Research Service calculates that the United States has spent nearly $750 billion on the war. (Remember when economic adviser Lawrence Lindsey was hounded out of the Bush White House for suggesting that it might cost $200 billion?) More than 4,400 U.S. service members have died and more than 30,000 have been wounded, and untold numbers of Iraqis have been killed, injured, or displaced. The U.S., and Iraq itself, are undoubtedly better off without Saddam. But many Americans are likely to lastingly agree with Joseph Nye, a former senior official at the State and Defense departments who now teaches at Harvard University's John F. Kennedy School of Government, when he says that the lesson of Iraq "is that the price of nation building ... is too high."

The bloody grind in Iraq showed the risks of panoramic aspirations.

In that way, the Iraq war may produce a deeply ironic result. Bush launched it at a moment when American power appeared unchallenged and American goals unbounded; in his second Inaugural Address, Bush declared that the U.S. would support "democratic movements and institutions in every nation and culture, with the ultimate goal of ending tyranny in our world." The bloody grind in Iraq showed the risks of such panoramic aspirations, and the danger of disconnecting ends from means and goals from capacities. For those who had forgotten, Iraq showed again "that no power is able to get everything it wants," as Nye says. That wasn't Bush's intent.

Even after Iraq, many Americans still resist any suggestion that the nation's ability to control world events faces limits. Senior Obama officials even recoil from using that word, for fear of inciting those who consider it a synonym for decline. But Obama has consistently argued for better balancing America's capabilities and commitments, prioritizing its goals, and enlisting more nations in building a secure international order. Apart from praise for the troops, the president's Iraq speech this week was scrubbed of triumphalism; close aides say that he hasn't changed his belief that the war was a mistake.

The world will inevitably frustrate many of Obama's own designs. The Israeli-Palestinian peace talks he commenced this week face a steep climb; Iran is still hissing; China isn't likely to soon stop belching greenhouse gases; and a recent international poll showed that America's image in the Arab world is again plummeting, despite Obama's concerted outreach. Above all, Afghanistan shows few signs of achieving the stability he seeks.

With international demands and domestic challenges proliferating, Iraq's message is that Obama must ruthlessly separate what America needs from what it wants in a world that doesn't easily yield either.