WASHINGTON — President Hu Jintao of China will arrive in Cannes, France, this week pondering a plea from Europe for tens of billions of dollars to help the continent get out of its debt crisis. And President Obama will arrive 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 are a stark example of waning American influence. Without the spare cash that Mr. Hu has at his disposal — and the power that can come with it — Mr. 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.