And President Obama arrived with a smile, some hearty handshakes, and his own plea: that Greece get its act together and that Europe fix its economic ills, which he has called one of the biggest drags on the United States’ own ailing economy.

The two contrasting appearances at the Group of 20 economic meeting were a stark example of waning American influence. Without the spare cash that  Hu has at his disposal — and the power that can come with it — Obama has struggled to cajole his own allies into taking the steps he believes are necessary to lift the global economy.

Yet the relative decline of the United States as an international force also comes with a silver lining. For decades, the United States has been the global rescuer of last resort. It is a role that has brought significant costs, both financial and human.

The last few months may well end up being an inflection point, in which the United States, though easily still the world’s leading power, no longer has quite the responsibility or the burden it once did. The pattern has been evident in the Arab Spring, with the American military playing mostly a supporting role in Libya, and now in the European financial crisis, with Asian money coming to aid the Europeans.

“Why would the United States want to have influence over a train wreck?” said George Friedman, the chief executive of Stratfor, a geopolitical risk analysis company. “If the Chinese want to provide $150 billion bailing out European banks, more power to them.”

In many ways, the situation is a natural evolution of the campaign promises made by Obama in 2008, when he vowed to turn away from the Bush administration’s more unilateral approach. As president, Obama is now overseeing the withdrawal of all troops from Iraq and has emphasised multilateral diplomacy in all its messy forms. He refused to consider American intervention in Libya until the United Nations approved a resolution supporting it, and then he stepped back and allowed France and Britain to take the lead though American military help remained essential.

Obama’s critics have decried the decline in American clout and said his approach exacerbated it, by forfeiting claims on American exceptionalism. Obama’s backers say that he is simply acknowledging reality and developing a clear-eyed strategy for what the US can and cannot do and that he ultimately may prove right in diagnosing Europe’s economic problems and its need to take difficult steps to fix them.

Premeditated move

“Obama has clearly made a premeditated move away from the unilateralism of the Bush years, and he’s done it because it’s the right way to conduct foreign policy, but has also done it because America’s leverage has been diminished,” said David J Rothkopf, a Commerce Department official in the Clinton administration and the author of “Running the World,” a book about the National Security Council. “We can’t write cheques the way that we once could; we can’t deploy troops in the way that we once did.”

But, Rothkopf argues, “we are in this situation of feeling overexposed and overburdened precisely because we had such an appetite before for unilateralism and triumphalism.”
For instance, he said, the staggering costs of the war in Iraq — which the US largely bore alone — contributed to the very same national debt and budget deficit that now prevent the United States from stepping in financially to help Europe.

Of course, in an election year, the last thing that Obama wants to be seen as doing is putting forward the idea that the US is no longer influential, or that there is no longer any such thing as American exceptionalism.

“This is a place that parents all over the world want to send their kids to university,” said Michael Froman, the deputy national security adviser for international economic affairs, during a briefing with reporters at the White House. “We’re the centre of innovation. We have a great network of alliances around the world that no other country has. I’m struck, in the G20 and the other forums that we’re involved in, I’m struck by the degree which other countries very much look to the US for leadership, thought leadership and leadership on action, to ensure a way to resolve global problems.”

In Cannes, Obama tried to balance providing that leadership while not taking on any of the additional burden — particularly financial — that such leadership often requires.

Whatever Democrats and Republicans may say about the United States’ role in the world, it is clearly changing. Over the last few days, American officials have watched, largely powerless, as the Greek government has threatened to undo the Europe-designed, Asia-financed deal to restructure Greece’s debts.

The White House press secretary, Jay Carney, all but shrugged when reporters asked him what the United States planned to do about the Greek prime minister’s surprise call for a popular referendum on a new debt deal with his country’s foreign lenders, a referendum that could throw Europe into even deeper turmoil. “It is a European problem that needs to be addressed,”  Carney had said, “and they have the capacity to do it.” Greece, of course, went back on its plan to hold a referendum.

The breakdown is a clear contrast to the 1990s, when the United States pushed through multibillion-dollar rescue packages for both Mexico and Asia, let alone the period after World War II, when the United States instituted the Marshall Plan.

But for all the acceptance that the United States will no longer be the world’s policeman and financier, the emerging strategy carries risks.

China, for instance, is bound to try to extract concessions from Europe for any aid, and the United States could end up losing Europe as an ally in pressuring China to take important economic steps of its own, like allowing its currency to float on the open market, which both European and American policy makers want.

And while the political appetite for myriad military adventures overseas might be on the wane in Washington, the American military remains the world’s most formidable, and the most likely to be called on to back American allies like Israel, Japan and South Korea.