Gone are the days when the US president could visit Beijing as the unassailable top dog, able to lecture the Chinese on everything from human rights to an overvalued currency. As has become fashionable to note, events have instead obliged Barack Obama to play the role of washed-up debtor visiting his stern bank manager for yet another loan.

That analogy is useful. But it can be overdone. Certainly, the financial crisis has brought into sharp relief just how dependent the US has become on foreign creditors, chief among them China.

It has also sharpened the perception of what had been happening anyway, the relative decline of a US-centric west and the relative rise of a China-centric Asia. But the word relative is important. China, poor and riddled with internal contradictions, is not there yet, by a very long way.

The changing relationship with China does demand a new tone. But early indications are that Mr Obama is still fumbling for the right one. Take global imbalances.

In the only set-piece speech of his Asian tour – delivered in Japan, perhaps to assure his hosts that Washington is not abandoning Tokyo just yet – Mr Obama correctly pointed out that the global economy cannot go back to business as usual. “One of the important lessons this recession has taught us is the limits of depending primarily on American consumers and Asian exports to drive growth,” he said.

That is quite right. But his entreaties on global rebalancing fall flat in China. That is partly because Beijing remains publicly sceptical about the US's long-term finances.

From China's perspective, Mr Obama's emergency measures to stimulate the US economy and persuade Americans to spend their way out of recession smack of re-creating the spendthrift ways that triggered the crisis in the first place.

That explains why Chinese officials have quizzed their US counterparts so robustly about how they intend to pay for healthcare reform. It is also why Beijing has started questioning US monetary, as well as fiscal, policy.

On the eve of the US president's visit, Liu Mingkang, China's chief banking regulator, took a swipe at the US Federal Reserve, saying the combination of a weak dollar and low interest rates risked generating a global asset bubble. That is a bit rich coming from someone who oversees a banking system that has pumped the equivalent of nearly 30 per cent of gross domestic product into the economy so far this year. But it reflects the new tone with which China presumes it can address a humbled superpower.

Mr Obama's efforts to occupy the moral high ground are also undermined by his flirtation with protectionism, particularly his decision to slap tariffs on Chinese tyres.

His administration has failed to spell out a convincing trade policy – and that is seen as a stark omission for a business-oriented Asian audience. Such perceived deficiencies have hobbled his ability to cajole China with any real conviction.

When it comes to human rights, too, the US seems to have drawn the conclusion it is not good policy to badmouth its chief creditor.

Hillary Clinton, secretary of state, set the tone early when she said that human rights should not “interfere” with matters of implicitly greater urgency. Mr Obama obligingly omitted all references to Tibet, Xinjiang and even Taiwan from his Tokyo speech. There was also not a single mention of India, a potential regional counterweight to China, yet another indication that Washington is behaving as though it is treading on eggshells. It was therefore all the more refreshing to hear Mr Obama criticise Chinese censorship during his town hall meeting in Shanghai yesterday – though even that could not undo his own self-censorship in refusing to meet the Dalai Lama before this week's trip.

It is right and proper that the US acknowledge the rising significance of China. Mr Obama's assurances that China's rise need not be a threat were spot on. But by the same token, US accommodation can be taken too far. Contrary to common perception, China's huge holdings of US treasuries are not a sign of great strength. They are evidence of how dependent Chinese growth has been on the US consumer.

Equally, any idea that China, with an economy less than a third the size of the US and a GDP per capita roughly the same as Angola's, can somehow save the world is ludicrous. Mr Obama is right to show respect to China. He need not – and must not – kowtow.