With Barack Obama now back in Washington after his first presidential tour abroad, fans and foes are rendering their verdicts on how he did. Did he show signs of emerging greatness? Or is he all presentation, the triumph of charisma over substance?

Some of the reviews have been raves. "(N)othing seems to be clouding the blue skies of the old continent's love story with President Obama," wrote French author Amélie Nothomb in last weekend's New York Times. "Mr. Obama's anger is portrayed here as something holy. And when he laughs, we laugh."

The flash of star power in London, the adoring crowds in Prague, the town hall meeting in Istanbul, and the surprise stopover in Baghdad have each added to the glow. Back home, the president's poll numbers have spiked. A new survey from The New York Times/CBS News gives Obama a 66 percent approval rating, his highest number yet.

Not surprisingly, some of Obama's Republican critics have raised their voices in dissent. Some charge that he pandered to foreign audiences during the visit and disparaged the United States. Others say he sacrificed American sovereignty in the name of international "unity." Commentator Dick Morris warned that Obama's work at the G20 summit amounted to repeal of the U.S. Declaration of Independence.

But beyond the predictable streams of adulation and derision, what did Obama really accomplish? He called on G20 members to coordinate economic stimulus packages, but French President Nicolas Sarkozy and German Chancellor Angela Merkel balked. He championed Turkey's bid to join the European Union, but Sarkozy and others said not so fast. Obama called on NATO allies to provide additional troops for the fight in Afghanistan. Obama will dispatch another 21,000 Americans. The rest of NATO promised just 5,000 more. Obama called on fellow permanent members of the U.N. Security Council to sanction North Korea following its latest provocation. Russia and China have said no.

We can now expect plenty of commentary that Barack Obama is an empty suit, a gifted orator but a lightweight on the international stage. Others will pin these problems on former President Bush and insist that Obama can't be expected to solve them in his first 100 days.

All these arguments miss the point. Bush is not entirely responsible for any of these problems, and no reasonable person can expect Obama to single-handedly resolve them. No U.S. president could. We must begin to accept that it matters less than it used to whether Americans have chosen their president wisely.

France and Germany have their own views on the costs and benefits of stimulus for their domestic economies. Several EU members question the wisdom of embracing majority Muslim Turkey -- and of extending the union's territory to the borders of Iraq, Iran and Syria. Many NATO members don't believe they can sell their publics on deeper commitment to the war in Afghanistan. Moscow and Beijing don't believe that new sanctions will make the Korean peninsula more secure.

Whether these governments are right or wrong, none of them need accommodate the U.S. president as they might have a decade ago. A floundering American economy, two expensive wars, public U.S. doubts about the benefits of free trade, and a broad range of unresolved domestic problems have diminished Washington's ability and willingness to play the role of world's only superpower. America's political, economic and military power will remain indispensable for years to come, but the age of post-Cold War triumphalism has passed. How else can we explain positive French reviews for an American president?

Yet, the major emerging powers face plenty of challenges of their own. European leaders are preoccupied with efforts to strengthen the EU from within -- and to guard against severe financial instability in Eastern Europe that might spread toward the West.

The Chinese leadership is grappling with the effects of reduced demand for its manufactured products in Europe and the United States. Beijing's $586 billion stimulus package and its around-the-clock efforts in Africa, Latin America, Central Asia and elsewhere to secure reliable long-term supplies of the oil, gas, metals and minerals needed to fuel further economic growth limit any temptation to take on a more assertive role in international politics.

Russian leaders are wrestling with the impact of the financial crisis on their country's banking sector, the creditworthiness of many of its largest companies, and the growing risk of civil unrest as workers lose their jobs or work without steady pay. They will continue to worry over events along Russia's borders -- in Ukraine, the Caucasus and the Baltic states, in particular. But the Kremlin has neither the cash nor the clout to accept the burdens and vulnerabilities that come with a greater international presence.

This is the real lesson from President Obama's foreign travels: The power of the U.S. president, any president, to build consensus behind solutions to international problems just isn't what it used to be. What's needed is a coordinated international approach to these challenges -- just at a moment when the governments of other powerful states are profoundly preoccupied with problems of their own.