After President Obama left Beijing Wednesday, I went to see the movie 2012 to learn more about China's growing role in the world and the corresponding emasculation of the American presidency.

For those readers who haven't seen the movie (spoiler alert!), China helps save what remains of humanity from an End of Days flood, building gigantic arks with incredible speed. "Leave it to the Chinese. I didn't think it was possible," says an awestruck refugee from the White House, which by this point has been obliterated along with the fictional black U.S. president.

Off the screen, we are familiar with this story: China saves the world; the U.S. is in decline. It is the popular refrain of the moment. China's economy will rescue us all from the global crisis. The U.S. is limping along, a shadow of its empirical self, relying on the largesse of its banker, China--the dragon rising, the tiger roaring, the panda waking.

This storyline dominated Obama's trip this week, informing seemingly every White House press corps dispatch: The president came to China, won no concessions on anything and didn't land a solid punch on human rights, certainly not compared with his recent predecessors. The balance of power has shifted dramatically.

There is some truth to this picture. Gone are the post-Tiananmen days when China came (sort of) begging to the world--for loans, for the Beijing Olympics, for entry into the World Trade Organization. Now the world is populated with supplicants, both companies and governments, coming to Beijing for Chinese money.

But all that doesn't suddenly make Obama a supplicant to President Hu Jintao. Obama played nice in public on Chinese soil because he is trying out something called diplomacy, and it may just be the right moment for it.

During all those years when the balance of power was heavily in favor of the U.S., China in reality gave up very little in real concessions on the big things, like human rights. China can release a political prisoner or two before a presidential summit, as it has many times, or it can detain and harass some dissidents, as it did this week. But the fundamental authoritarian system obviously remains unchanged, continuing to pressure, intimidate and lock up dissidents, perpetually creating new political prisoners who can be released as bargaining chips someday.

The U.S. still practices "prisoner diplomacy," which is certainly the right thing for the brave individuals it can help. But Obama has made clear he wants to forge a different kind of long-term relationship with China, one that relies less on bargaining chips and more on building good will.

An easy way to do that is to be polite and respectful in your public appearances. Obama could have come to China and wagged his finger at Hu in front of the cameras, saying dramatically, "Mr. Hu, tear down that Great Firewall," as some Chinese netizens wanted him to do. It might have sounded good, but good luck getting much cooperation from China for a long time after that.

In 1998, then-President Clinton made a point of bringing up the 1989 massacre near Tiananmen Square on Chinese national television, in a joint appearance with his host, President Jiang Zemin, who rose to power amid that bloody crackdown. Given that this was the first presidential visit since 1989, Clinton probably made the right move, sending an important signal to Chinese leaders, the Chinese people and the world that the U.S. still makes human rights a priority.

Today the context is different. China has indeed risen and the U.S. is reeling, but more important, the U.S. needs China's help in a world that seems more dangerous now than it did then. Obama does need to talk tough with Hu, especially about Iran's nuclear ambitions, but he may get better results by doing so in private, and I suspect he gave it his best shot Tuesday.

Will this brand of diplomacy work? Maybe not. Former Ambassador to China James Lilley, who died last week, believed that going easy on China in public gained you nothing. Lilley "used to say that you've got to take a tough position and then you engage in tough negotiations," says Jim Mann, author of About Face, a history of U.S.-China relations. Mann, having chronicled many instances of the U.S. having emerged empty-handed from negotiations, isn't persuaded that playing nice in public gets results.

But there's a flip side to the rising China story. Yes, Chinese leaders have a lot more leverage now, but they also have a lot more to lose if the world goes haywire. Obama sees that when he acknowledges China's growing role in global affairs. As he asks for help in the United Nations, possibly soon, with tougher sanctions on Iran, it could start getting harder for Beijing to say no.