BEIJING — When China’s vice president and presumptive next president, Xi Jinping, arrives at the White House on Tuesday, American leaders will be scrutinizing him for hints of future stances on crucial issues, from Chinese military intentions to the nuclear programs of Iran and North Korea.

But none is more important — and for now, more opaque — than the question of where Mr. Xi and the next generation of leaders want to take China’s economy, which is still growing rapidly but shows signs of stress and structural instability, economists say.

Mr. Xi’s cross-country swing, from Washington to an Iowa farm town to Los Angeles, comes at a politically charged moment in American relations with China. China’s economic competition with the United States has already become a theme in this year’s Republican presidential primaries, and President Obama has toughened his tone on Chinese trade and fiscal issues.

In meetings with Mr. Xi at the White House on Tuesday, a stock list of economic demands — that China lower barriers to American investment, build a consumer-driven economy that would buy more American imports and allow the renminbi to rise against the dollar more quickly — seems likely to dominate Mr. Obama’s side of the conversation, according to officials in Washington.

For his part, Mr. Xi, introducing himself to the American public, will showcase a down-home personality in contrast to that of China’s stoic current president, Hu Jintao. He will announce some business deals with American companies and, like every Chinese visitor, pledge to improve bilateral relations. But given the domestic pressures over this year’s once-a-decade leadership transition in China, the odds that Mr. Xi will accede publicly to Mr. Obama’s requests are practically nil.

There is a longer-term debate about reforms going on even now, however. In recent months, some Communist Party elites have privately debated the necessity of those reforms with renewed vigor; some of the discussion has crept into public discourse, and there are a growing number of attacks by intellectuals and former officials on what they call the “vested interests” that threaten to take China further down the road of crony capitalism.

But the delicacy of the leadership transition and the structural limits on Mr. Xi’s authority, particularly in his first five-year term in office, would hamper attempts by him or his colleagues to push reforms even if they are inclined to do so.

He and a new leadership team are set late this year to inherit a quasi-market economy geared above all else to generate fast growth.

The state-owned industries that have ballooned in size, the coastal provinces that have grown rich on exports, the local governments that have reaped billions from land sales and poured billions more into building glittering cities — all have interests in that economic policy. Economists agree that reforms are needed to land ownership, the social welfare system and the financial sector, and that China must overhaul its investment-driven growth model, but all of that would work against those interest groups.

The big state corporations, in particular, have gained political clout alongside their wealth. They have monopolies on the most important industries — banking, oil, aviation, construction, telecommunications — and they maintain close ties to the top party officials. Two former executives of mammoth oil and machinery companies sit on the current Standing Committee of the Politburo, the nine-member body that essentially runs China by consensus.

The officials expected to take posts on the Standing Committee this October all have ties of some kind to the heads of state enterprises; for example, Wang Qishan, who is seen as relatively liberal on economic policy, was a top state bank executive himself. Corporate executives regularly rotate into top provincial posts, and still more sit on the Communist Party’s Central Committee.

“If the new leadership can crack down or curtail these companies, they will score well with the public. But those interest groups are very powerful,” Cheng Li, a scholar of elite Chinese politics at the Brookings Institution in Washington, said in an interview. “The political risk is overwhelming.”

So, say some, is the risk of doing nothing. Concern has mounted in some quarters of the party — and anger among citizens — over the emergence of a powerful and privileged elite. Cynics have coined the phrase “black collar” to describe the big-city titans and government elites who wear expensive black suits and invariably drive black luxury automobiles, often flouting traffic and speed laws.