Hillary Clinton’s Beijing agenda is growing longer and more daunting by the minute.

Everywhere the U.S secretary of State looks in today’s China-U.S. relationship, tensions that might unnerve markets or fracture strategic relationships stare back at her. Strains were building even before blind activist Chen Guangcheng reportedly took shelter in the U.S. Embassy in Beijing after a bold escape from house arrest. Finessing the U.S.’s role in the scandal surrounding ousted Communist Party Politburo member Bo Xilai and his family would have been challenge enough for Clinton’s team.

The same goes for China’s early support for the brutal Assad regime in Syria, the U.S. sale of F-16s to Taiwan, disputes over Iran, America’s embrace of Myanmar and Beijing’s military ambitions. Then there are the formidable challenges facing Treasury Secretary Timothy Geithner, who is accompanying Clinton for the May 3-4 talks: currencies, intellectual property rights, trade and investment.

The world’s most-vital economic relationship hasn’t been this fraught with potential conflicts and points of disagreement in years. It will take deft and visionary statecraft to keep today’s headaches from damaging the future workings of the so-called Group of Two.

Yawning Divides

Financial markets are used to Washington and Beijing finding areas of agreement and downplaying the yawning divides between their economic demands and aspirations. The trouble is we’re fast running out of the easy areas of agreement.

The political climate limits the maneuvering room for leadership in both countries. This year’s U.S. presidential election coincides with the expected ascent of Chinese Vice President Xi Jinping as the replacement for Hu Jintao. Xi won’t enjoy the honeymoon typically afforded new presidents. Not with his economy slowing, China’s rich-poor gap widening and the Communist Party beset by the biggest challenge to its legitimacy since the 1989 Tiananmen Square crackdown on pro-democracy protesters.

The state of economy is paramount to China’s leaders. The social contract is this: We will make you wealthier, and you don’t head to Tiananmen with protest banners. Yet China is feeling the strain of a world economy in turmoil at a time when its leaders fear an Arab Spring-like uprising at home. The benefits of the hundreds of billions of dollars China tossed at the economy since 2008 have worn off. All that’s left now are asset bubbles, debt and several hundred million people wondering why incomes aren’t rising faster than living costs.

The easiest remedy would be devaluing the yuan anew to boost exports. Doing that would antagonize President Barack Obama and the presumptive Republican nominee, Mitt Romney, but China may decide the end justifies the means. The same goes for the piracy that so angers the Walt Disney Co.’s and Apple Inc.’s of the world. For better or worse, selling fake DVDs, sneakers and electronics creates jobs. So does bending the World Trade Organization to China’s benefit at the expense of everyone else.

Anyone who thinks Beijing and Washington will see eye to eye on these and other issues is in denial. China knows that, barring a major crash, it’s destined to surpass the U.S. economy the way it overtook Japan. Europe, after all, is turning to China to bail out its failed single-currency experiment.

Beijing also knows what the U.S. has been slow to grasp: American soft power is waning. Few countries aspire to the U.S. model of capitalism after the demise of Lehman Brothers, and the shame of the prison at Guantanamo Bay, Cuba, undermines any claim to moral high ground. Chinese tolerance for lectures from Americans on free markets and human rights is low.

Dollar Concerns

That goes for the dollar, too. China sees Federal Reserve Chairman Ben S. Bernanke’s ultralow interest rates as a de facto devaluation. That suspicion weakens U.S. argument for China to revalue. It also touches on the prickly topic of China’s vast dollar holdings. The U.S. currency is a crucial component of China’s $3.3 trillion of reserves. Anything that depresses the dollar will enrage China.

Yet China’s fragility was very much on display this week. The Chen story may get the most headlines. China abhors anything it perceives to be foreign meddling in its affairs. Reports that the U.S. is sheltering the human-rights activist must have Beijing powerbrokers doing back flips. The real fireworks, though, may involve the spectacular fall of former Chongqing bigwig Bo.

The U.S. was drawn into a sordid tale that involves allegations of corruption, greed, murder and wiretapping of top officials. The story spun out of Beijing’s control and made headlines worldwide when Bo’s former police chief sought asylum in a U.S. consulate while claiming that Bo’s wife was involved in killing a British businessman. China is abuzz with conspiracy theories about a U.S. campaign to foment discord. This scandal is nothing short of a political earthquake.

The importance of maintaining constructive U.S.-China relations is lost on no one. The G-2 is the linchpin of an unsteady world economy, and keeping the peace is vital to averting financial upheaval and restoring growth. Yet Clinton, Geithner and their Chinese counterparts may find that ensuring the status quo is beyond their grasp.

(William Pesek is a Bloomberg View columnist. The opinions expressed are his own.)

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To contact the writer of this article: William Pesek in Tokyo at wpesek@bloomberg.net.

To contact the editor responsible for this article: James Greiff at jgreiff@bloomberg.net.