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Diplomatic visits by heads of state are mostly symbolic affairs, concerned less with ironing out differences than with paying respects in a formal, stylized setting. In that sense, China President Hu Jintao's upcoming trip to Japan — the first by a Chinese head of state since 1998 — is expected to be run of the mill. The meticulously scripted itinerary calls for Japanese Prime Minister Yasuo Fukuda to play host as Hu strolls through Yokohama's Chinatown, visits temples in Nara and dines at the Imperial Palace. On May 8 at Waseda University in Tokyo, Fukuda's alma mater, the two leaders are scheduled to play Ping-Pong.

A gracious host would throw the match, but Fukuda might want to think twice before dropping his paddle: a display of national athletic prowess against an old rival might be just the tonic he needs to revive his moribund prime ministership. Since taking over from the hapless administration of Shinzo Abe in September 2007, Fukuda's team has managed to look even more inept and out of touch than Abe's on issues ranging from Japan's faltering economy to the appointment of a new central-bank governor. Initiatives by Fukuda's Liberal Democratic Party (LDP) have been bottled up in parliament by resurgent opposition politicians. Recent polls have put Fukuda's public approval rating at about 25% — lower than Abe's before he resigned after less than a year in office. "When [Fukuda's] approval breaks below 20%, he's really in deep trouble," says Gerald Curtis, a political-science professor and Japan specialist at Columbia University. "That can happen and I bet he's holding his breath."

Fukuda's precarious situation makes it especially important that Hu's visit goes smoothly. Since hitting a low point in 2005, when thousands of Chinese staged anti-Japanese protests in major Chinese cities, typically frosty political relations between the two countries have been warming up a bit — and because of China's growing economic power, it's crucial to Tokyo that this trend continues. (China last year surpassed the U.S. as Japan's largest export destination.) Like Abe, Fukuda has avoided angering Beijing by refraining from official visits to the Yasukuni Shrine, which honors Japanese war dead, including 14 convicted Class-A war criminals from World War II. But the delicate relationship between China and Japan contains many potential flash points, among them disputed exploration rights to gas deposits in the East China Sea and a disagreement over how pesticide-laced, Chinese-made dumplings wound up in Japanese stores.

And then there are the troublesome T's: Taiwan and Tibet. "Clearly Hu Jintao would like the Japanese to line up and say that they oppose Taiwan's independence, but there's too much opposition to that from within the LDP," says Curtis of Columbia University. Experts expect Fukuda will go no further than stressing the importance of a peaceable resolution. While Fukuda may be able to manage the dialogue on Taiwan, it will be harder to control the Japanese public. A rash of pro-Tibet demonstrations by the country's Buddhists could embarrass Hu, who has been trying to quell dissent over China's rule in Tibet in the run-up to the summer Olympics in Beijing. Noisy protests in Tokyo "would be impossible for Fukuda to ignore," says Curtis. "It would really throw a damper on the visit."

If the summit goes well, though, Fukuda could yet turn around his struggling administration. Abe, his predecessor, was most popular right after his successful visit to Beijing in October 2006. Similar good vibrations could give the current Prime Minister time to reshuffle his Cabinet and survive until July, when the spotlight will be on Japan as it hosts a G-8 summit. That could "slow the erosion of [Fukuda's] support," Curtis says. "That's what he has to do if he's going to stay in office much longer." Says Phil Deans, an international-affairs expert and assistant dean at Temple University in Tokyo: "The more ordinary, normal and boring the Sino-Japanese relationship is, the better it is for everybody." When Fukuda takes on Hu at Ping-Pong, his shot selection had better be perfect.

• Coco Masters/Tokyo