Meeting Japan's emperor and empress, Obama bowed low, as well as shaking the hand that the emperor offered. His action was accepted in Japan as awkward but gracefully polite. In the US, it set off howls of protest from right-wing Republicans that an American president should bow to no one. Pundit William Kristol said it showed that the US was becoming weak and deferential. To prove their point, critics juxtaposed a picture of former vice-president Dick Cheney greeting the emperor in 2007 - a firm handshake, no bow.

How a president should greet an emperor is a tricky issue of protocol that should not get in the way of real policies. But the reaction of America's loony right shows that they are just as mad about missing the real point as the Loony Left ever were. The answer is to laugh and move on, except that the Republicans are being led by the loonies and determined to damn everything Obama does. The question is whether ultrapoliteness may undermine efforts to update policy.

Shortly before Obama arrived in Japan, a 66-year-old man in Okinawa was killed by a hit-and-run driver from the nearby US base. Since 1952, US troops have been involved in more than 200,000 accidents and crimes, involving more than 1,000 deaths and well-publicised cases of rape of underage girls. The hit-and-run death again raised fierce local opposition to the presence of US troops.

To get back to the facts on the ground, Obama's visit highlighted that the Hatoyama government wants to make its mark and create a new foreign policy that sees Japan less in thrall to the US and more of a player in its Asian home. This will accord - belatedly - with Japan's huge global economic footprint.

Unfortunately, setting out the agenda of ambitions is proving difficult enough, let alone realising them. Hatoyama's Democratic Party of Japan did not set out a coherent vision in its election manifesto. Depending on your point of view, this is a minor matter - because a manifesto is not a sacred document that any parliament or court will attest to; or a major one - because to make a radical change without spelling it out means it lacks legitimacy.

The DPJ won the election because voters were tired of the previous Liberal Democratic Party government that had run out of ideas and leaders, rather than because of any great enthusiasm for the new party. Nevertheless, the DPJ will inevitably scrap the baggage of decision-making that the previous government used. It has to.

But revising Japan's foreign relations is tough because there is a profusion and confusion of views both on the general vision and on the specifics. Hatoyama himself has been doing his best to work towards a coherent policy on all the fronts, including relations with the US and Japan's place in a newly emerging and prosperous Asia.

Hatoyama lives under the dark shadow of Ichiro Ozawa, the party secretary general and mastermind, who would have been the prime minister had he not been snared in a corruption scandal involving a close aide. Ozawa has long held that Japan must become a more 'normal' nation and, just before Obama arrived, he made extraordinary remarks barely noticed in the West, damning Christianity and the West as 'exclusive and self-righteous'. He added that 'Islam is better, but it is also exclusive'. Buddhism is his preferred way.

On the other side, Japan is restricted not merely by history but by existing treaties. The overriding agreement is the Treaty of Mutual Co-operation and Security between the United States and Japan, signed in 1960, with such outbursts of hostile popular feeling that president Dwight Eisenhower cancelled a visit to Japan and prime minister Nobusuke Kishi resigned. The treaty pledges the US to come to Japan's assistance if it is attacked and its Status of Forces of Agreement (Sofa) allows US troops and bases in Japan, funded largely by Japan. Sofa is regularly revised, most recently in 2006.

The number of US troops stationed in Japan has fallen to about 36,000. Most of the US bases have now been pushed to the southern islands of Okinawa, where resentment of the US military is intense because of aircraft noise, pollution and the behaviour of some troops. Under the US$26 billion 2006 deal, 8,000 US marines will be deployed to Guam and the Futenma air station will be relocated on Okinawa. The new DPJ government is unhappy with the deal, not least because Okinawa elections are due next year.

Obama's US seems to regard Japan as rather tiresome because its main eye is on China. Defence Secretary Robert Gates warned this month that, if Japan resisted a deal, the US would halt the deployment to Guam and refuse to give back land. Obama offered an olive branch of a high-level working group to consider the deal but, when it met this week, the US side simply wanted to get on with the details, to Hatoyama's irritation.

Both countries have to be careful: the US risks losing a friend that should be cultivated rather than snubbed; Japan needs to be careful because the state of its government finances mean it cannot afford to discard the US defence umbrella soon.

Kevin Rafferty is a political commentator