Or perhaps "giant panda in the room" would better fit the context.
Mr. Obama will not touch down on Chinese soil, but at every stop he does make – from India to Japan, with Indonesia and South Korea in between – China and its economic, political, and military rise will either explicitly or implicitly figure on the agenda.
•In India, Obama will hear of Indian concerns about China's strengthening ties to – and plans to sell nuclear reactors to – rival Pakistan, even as the United States and India discuss a mutual interest in seeing China's rise occur peacefully.
•In Indonesia, the discussion will turn to China's growing naval and shipping presence in key trade and strategic maritime routes.
•South Korean leaders will want to address China's unflagging support for an increasingly aggressive North Korea, even as Obama takes the issue of China's trade practices and currency manipulation to a Group of 20 summit in Seoul.
•In Japan, China's growing assertiveness on everything from economic issues to territorial disputes is sure to be an item on the bilateral agenda and at a summit of the Asia-Pacific Economic Cooperation forum.
"China is going to be the apparition at the table of discussion at every one of Obama's stops on this trip," says David Lampton, director of Chinese studies at Johns Hopkins University's School of Advanced International Studies in Washington.
The No. 1 topic in all of these countries will be the US economy and prospects for a return to sustained growth, Mr. Lampton says, given the importance the US has as a market for the region's exports. But the leaders Obama meets will have one overarching question on their minds, he adds: Will the US be a long-term counterbalance in the region as China continues its rise?
"All of these countries are looking for an equilibrating force in the region," Lampton says, "and in that context they are looking to the US and asking themselves if the US is going to be around, and in what role."
The Obama administration has stressed its efforts to improve US-China relations, but what the administration has billed as working with China has repeatedly been tagged as accommodating China by critics at home and in the region.
More recently, as China boomed through the global recession and increasingly adopted what Washington perceived as aggressive stances in security and territorial disputes with neighboring countries, the administration has shifted its posture. By visiting four of Asia's major democracies and taking up the trade and security issues topping the agendas of China's smaller neighbors, Obama is signaling an intention to maintain robust American leadership in Asia, regional experts say.
Administration officials insist they want to maintain strong cooperation with a rising global power, but at the same time the president's trip is seen as the appropriate occasion for assuaging the region's concerns about both China and continuing US leadership.
"I think most everyone in Asia appreciates the need for a cool-headed, constructive diplomacy between the United States and China in the current environment," said Kurt Campbell, assistant secretary of State for East Asian and Pacific Affairs, at a recent briefing with reporters. "We're also working closely with a number of states in the Asia-Pacific region, most prominently to underscore the strong US commitment to remain an active and engaged diplomatic, political, security, and economic player."
South Korea, where Obama will spend two days largely focused on the G20 summit of developed and emerging economies, is a prime example of a US partner warily watching China's growing shadow.
China is the South's largest trading partner – imported Chinese cabbage recently came to the rescue when a dearth of home-grown cabbage left distraught Koreans without kimchi, their beloved national dish. But the US, which is now the South's fourth-largest trading partner, remains its vital security guarantor, not only against the volatile North, but more subtly in the neighborhood of a rising China.
The potential for growing friction with China is a key reason the South Korean government values approval of the stalled Free Trade Agreement (FTA) with the US – as much or more as a sign of a strategic US commitment to North Asia as for its economic potential.
"We need more US engagement in Asia – especially in North Asia – as a stabilizing force. One of the more salient examples of that stabilizing presence would be through the FTA," said South Korea's ambassador to Washington, Han Duk-soo, at a recent dinner with Washington reporters.
Ambassador Han did not overtly link his country's desire for an American "stabilizing force" in the region to a rising China, but South Korean diplomats do so privately. One diplomat, discussing Obama's trip, referred to a cold-war era "equilibrium" of major powers that South Koreans fear could be lost, adding that the South is "looking for reassurances that the US will remain a balancing power in our region."