For Hu, it was a ‘legacy’ visit, his swansong as the head of the world’s most populous and potentially most powerful nation before stepping down as the leader of the Communist Party of China in 2012. The Obama White House obliged by allowing him to make the first state visit to the White House since a state visit by Jiang Zemin in 1997.

This too is not surprising. During the past year, China’s image and soft power have taken a battering, especially in the Asia Pacific, where it rekindled mistrust by asserting claims over the South China Sea, refusing to condemn North Korea for its aggressive tactics towards the South and restricting exports of rare earth elements. The US has gained considerable mileage out of these Chinese missteps, despite the Chinese snub to Obama at the Copenhagen climate talks in December 2009, and Beijing’s harsh condemnation of the $6.4 billion US arms sale to Taiwan and the Dalai Lama visit to the White House. As fears of China are rekindled in Asia by Beijing’s own assertiveness, there is a new recognition of America’s role in the region’s security. The Obama administration could thus afford to look generous and reward China for taking some conciliatory steps in the months leading up to the Hu visit — like letting its currency appreciate a bit, and hosting a visit to China by Defence Secretary Robert Gates.

But for those who see the US and China as leaders of the 21^st century global order, the summit holds an important lesson: while the uni-polar moment in international relations is over, it will not be replaced by a China-US duopoly, at least not an effective one that addresses the global challenges of our time.

No one can deny the power shift, although the US President did try. At their joint press conference, Obama told the visitor (and more the American people perhaps): ‘What we have to remind ourselves is that the United States’ economy is still three times larger than China’s, despite having one-quarter of the population’. But just over a decade ago, in 2001, the US economy was more than seven times larger than China’s.

To be sure, the US-China relationship is often touted as the most important relationship for the future of the world. But the Hu visit made two things very clear. First, America’s domestic politics would prevent the two sides from developing the trust needed for that, and, second, issues in the bilateral relationship take priority over tending to the problems of the world at large.

Even as the White House prepared to welcome Hu, across the Mall the Congress fumed by holding a hearing on human rights in China and blaming it for the largest number of political prisoners in the world (allegedly ‘millions’). The newly anointed speaker of the House of Representatives, John Boehner, refused the invitation to the White House dinner. And in a show of bipartisanship that has all but vanished these days, Senate Majority leader Harry Reid called Hu a ‘dictator’.

The thrust of the entire visit has been bilateral issues, America’s trade deficit, China’s currency manipulation and, of course, China’s abysmal human rights record. Hu seemed more conciliatory than usual on human rights, keeping in mind his visit to Congress later in the visit. After initially avoiding a question on the subject (because of a translation glitch) at his joint press conference with Obama, Hu conceded in a follow-up that: ‘A lot still needs to be done in China in terms of human rights. We will continue our efforts to improve the lives of the Chinese people, and we will continue our efforts to promote democracy and the rule of law in our country’. But he also asked ‘to take into account the different and national circumstances when it comes to the universal value of human rights.’ The joint statement noted ‘significant differences’ over the issue, especially the Chinese insistence that ‘there should be no interference in any country’s internal affairs’.

Over global governance issues, Hu mentioned at the press conference China’s support for the G20 to play ‘a bigger role in international economic and financial affairs’, and to ‘work with the United States and other countries to effectively address global challenges’ such as climate change and terrorism.

By all indications, the United States is coming to terms with the end of its ‘G1’ world, although it is still impolite to mention the ‘D word’ (decline). Although Secretary of State Hillary Clinton did talk about ‘the new American moment’ in international affairs, it was a call for sharing the burden with others, including emerging powers — China being one but not the only one of them. It also called for working through global and regional institutions to advance American interests.

When the United States replaced Britain as the global hegemon after the end of World War II, it did not shy away from accepting international obligations and making sacrifices. Why is China not following the US path to global leadership, albeit a shared one with the US?

When the US under the Bush administration was riding high in the uni-polar moment, China was (secretly) thrilled to be counted as the main challenger to US dominance. Many Chinese still do, but being a challenger is not the same as being a leader.

Some blame it on Deng Xiaoping, China’s late paramount leader, who is supposed to have warned against China becoming a leader in the world. But this is a myth. Deng was more nuanced and qualified, and China today is far more powerful than during Deng’s time. The Chinese are scared of global leadership because they it see it as a ploy to force them into prematurely accepting responsibilities that will undercut their ‘peaceful rise‘. The idea of a joint leadership with the United States has been dismissed not because China does not want it, nor because they do not think they are up to it. They dismiss a ‘G2’ branding because it calls for sacrifices that they are unwilling to make, like accepting significant binding cuts in their carbon emissions.

However, there is a silver lining here. If the burden of domestic politics and bilateral mistrust limits the ability of the US and China to jointly manage global issues, it leaves room for others — Canada, India, Europe and other G20 nations — to step in and have their say. This may not be such a bad thing.

Amitav Acharya is Professor of International Relations, School of International Service, American University and Senior Fellow at the Asia Pacific Foundation of Canada.