The head of Boeing chose his words carefully as he explained to U.S. President Barack Obama the dilemma that Corporate America faces in trying to do business in China.

We see a world where our interests lay in both competing with China ... and also engaging with China for access to its market, Jim McNerney, Boeing Co's chief executive officer, said on Saturday as he interviewed Obama at the APEC business leaders' summit.

How would you assess the U.S.-China relationship when voices now on both the left and the right are calling for a harder line from your administration?

Obama did not miss a beat, providing a perfectly bland response that there can be friendly and constructive competition between the world's two biggest economies.

But Obama clearly took Corporate America's concerns into consideration when he met privately with Chinese President Hu Jintao on the sidelines of the Asia-Pacific Economic Cooperation forum on Saturday.

He made it very clear that the American people and the American business community were growing increasingly impatient and frustrated with the state of change in China's economic policy and the evolution of the U.S.-China economic relationship, said Michael Froman, a senior White House adviser on international economic affairs.

A day after his tete-a-tete with Hu, Obama laid on another layer of criticism before a bank of television cameras. He said the relationship was off kilter and China was too grown up now to flout international rules.

Obama's aides have said the president reserves his strongest language on China for closed-door meetings, so it was unusual to hear such sharp words made public. Rebuking Beijing publicly can backfire because Chinese officials are loathe to give the impression they are bowing to U.S. pressure.

The tougher U.S. tone is all talk for now. But if American companies conclude the cost of doing business in China outweighs the benefits, it could herald a fracturing in the world's most important international relationship.

China's undervalued currency and lax protection of intellectual property top the list of business complaints. Obama regularly raises those issues.

On the other side of the equation are China's estimated 300 million middle-class consumers, a population almost as large as the entire United States and a potential gold mine for U.S. businesses looking for faster growth.

Judging from comments by executives this week, many still see more opportunities than obstacles in China. In a poll of executives prepared for the APEC summit, more than 40 percent said their single greatest growth opportunity comes from the rise of spending power in Asia, particularly China.

But Obama made it clear he is hearing complaints from executives over difficulties in gaining fair access to China's markets and protecting intellectual property. It appears that Corporate America's patience with Beijing is wearing thin.

U.S. businesses are increasingly pessimistic about their trajectory in China and as a result the Obama administration has more support behind openly criticizing China's trade policies, said Nick Consonery, an Asia analyst with political risk consultants Eurasia Group in Washington.

PLAZA ACCORD 2.0

It was businesses that lobbied hard for the United States to get tougher with Japan in 1985, accusing Tokyo of keeping the yen artificially low to assist its exporters and putting American companies at a competitive disadvantage.

The result was the Plaza Accord in which Japan agreed to allow the yen to appreciate more rapidly.

Some in Beijing believe the United States is angling for Plaza Accord 2.0, this time aimed at the Chinese yuan. They blame the 1985 deal for sowing the seeds of Japan's lost decade of economic growth and fear the United States wants China to suffer a similar fate.

When the U.S. Senate passed legislation designed to press China to let its currency rise more rapidly, Chinese officials warned it could trigger a trade war if it became law.

But there is no indication the United States is considering anything like a Chinese Plaza Accord.

Back in 1985, heavy equipment maker Caterpillar was among the most active in lobbying Washington to get tougher with Japan. Now, its executives are pushing for diplomacy.

The worst thing we can do is encourage a process that may result in some sort of trade friction or a trade war in the two largest economies in the world, Caterpillar Inc President Rich Lavin said.

At Caterpillar, we're really encouraging continuing behind-the-scenes discussions and negotiations to move China towards a stronger currency.

The Obama administration has also struck a conciliatory note in public on the yuan issue. Treasury Secretary Timothy Geithner repeatedly states Beijing recognizes that a stronger yuan is in its self-interest and is prepared to allow further appreciation -- a point he made once again at the APEC summit.

The real disagreement lies over the pace.

The yuan has risen 7 percent against the dollar since June 2010, when Beijing loosened its grip on the tightly managed currency. Adjusted for inflation, the rise is nearer 10 percent.

Geithner and Obama have both said more is needed. But Wei Jiafu, chairman of China's largest shipping conglomerate China Ocean Shipping (Group) Co, said a swifter yuan rise would hurt exporters and drive up unemployment, and Beijing is sensitive to that concern.

The currency is the most visible manifestation of a much more complicated economic relationship.

Market access is a bigger issue for U.S. multinationals. Many complain the playing field is tilted towards China's state-owned enterprises and China does too little to protect intellectual property.

The business community has moved from devoutly trying to protect U.S. access to the Chinese market to wondering whether there is that much access to the Chinese market in the first place, said Derek Scissors, a research fellow at the conservative Heritage Foundation in Washington.

Scissors sees the shift as more a reflection of the weak U.S. economy than any stark changes in China's policies. After the financial crisis struck, companies simply were not making as much money in China and that soured the relationship.

The market access complaints are not entirely one-sided.

Wei, the COSCO chairman, said the United States denied his company's request to build U.S. ports capable of docking large Chinese container ships.

Right now, American companies in China are already doing fair business, Wei said, noting China offers tax breaks to encourage foreign businesses to invest.

WHAT HAPPENS NEXT?

Some of the friction can be traced to U.S. politics. Knocking China plays well among U.S. voters, so it is not surprising to hear sharper rhetoric as the presidential election in November 2012 draws nearer.

Candidates on the campaign trail tend to say strong things and if they win they tend to take more balanced positions, Singapore's Prime Minister Lee Hsien Loong said, when asked about anti-China sentiment in the United States.

But if America's economy remains weak, tensions may not ease after the election.

Robert Kapp, a former president of the U.S.-China Business Council, said the extent to which Western capitalism fell on its rear end during the financial crisis altered the relationship between the two countries.

There's a different psychological landscape, he said. No one can get a job in the West and the Chinese economy is growing at 9 percent a year.

Likewise, if China's economy suffers a sharp slowdown then Beijing may be more inclined to promote its state-owned enterprises at the expense of U.S. business.

China is becoming more enamored of industrial policy as a tool of accelerated development and I find this very troubling, said Charlene Barshefsky, who was the U.S. trade representative when China joined the World Trade Organisation a decade ago.

The Chinese government needs to better appreciate that, in both letter and spirit, its obligations are put at risk when it engages in activity that benefits domestic enterprises at the expense of competition and at the expense of foreign enterprises, she told Reuters in a recent interview.

For now, the message from U.S. businesses is that Washington ought to keep up the pressure but perhaps not squeeze too hard.

My urging is that these (tensions) be resolved through diplomacy and with cool heads, said Eli Lilly chief executive John Lechleiter.

(Additional reporting by Doug Palmer, Michael Martina, Stella Dawson, Rachelle Younglai, David Lawder, Caren Bohan and Laura MacInnis in Honolulu; and Lucy Hornby in Beijing; Editing by John O'Callaghan; )