Presidents Barack Obama and Xi Jinping won’t be the first notables to check into the sprawling Sunnylands estate in Southern California in search of seclusion and a chance for private chat. Among others, Queen Elizabeth, Bob Hope and Frank Sinatra beat them to it.

But the June 7 and 8 talks between leaders of the United States and China, representing the world’s two largest economies, will be the most substantive ever staged at the “mid-century modern” playground for the rich and famous built by the late billionaire Walter Annenberg. The meeting will bring together two politicians struggling, with varying success, to seize hold of their respective governments and shape policies despite domestic problems that can seem overwhelming. Partly because the summit has been scheduled as a “shirt-sleeves meeting” shorn of diplomatic frills, and partly because both presidents can use a success—President Xi says they are meeting at a “critical juncture” in the relationship—the results could far exceed the usual bland communiqué and provide firmer guidelines for future relations.

The goal is not to negotiate specific agreements about tactical matters but to reach general understandings about how the two governments intend to deal with each other on strategic political, economic and security issues. Some analysts fear they have been, intentionally or not, drifting toward an era of increased tension or even confrontation. The Sunnylands meeting is meant to reset things without getting bogged down in details. As China’s ambassador in Washington, Cui Tiankai, has said, the meeting “will not have a long list of deliverables” but the two sides “have determined they will work together to build a new type of relationship.”

There are early signs that something useful will result though there are no guarantees. The two presidents head political systems that share a mutual distrust, yet also a growing awareness that they need each other for their separate reasons.

As the talks draw near, President Obama’s problems are well known. A dysfunctional Congress that includes House Republicans determined to block almost anything he proposes, scandal at the Internal Revenue Service, apparent assaults on press freedom and an economy that merely limps along would be on anyone’s short list. In addition, there’s not much on the foreign front that brings him credit these days; violence in Syria and across the Mideast dominates the news, causing many Americans to blame him for not doing more to sort it out while others are afraid he’ll try. Something good with China would help him change the subject to his advantage.

Less well understood, at least for Americans, is that President Xi faces even more fundamental problems though not political ones of the democratic sort. As head of a one-party state run by Leninist rules, Xi has no balky parliament or overt rivals to impede him as either general secretary of the Communist Party or the nation’s president. But domestic pressures limit his ability to take daring initiatives, even though they also increase his need to show achievement. Growing public cynicism about Communist Party corruption and other malfeasance gives him a vested interest in trying to create what he calls “a new type of great power relationship” that could bring him great prestige inside China.

Perhaps Xi’s greatest challenge is a growing disaffection between the party and the people, one that leaders fear might eventually put at risk both social stability and their own political control. The more egalitarian aspects of Mao Zedong’s legacy were jettisoned long ago—the chairman’s own granddaughter is one of the richest women in China—and the ruling system is riddled with corruption, cronyism and nepotism. High-handed officials who enrich themselves in office dominate party structures from top to bottom, often in collusion with friends and relatives who control state-owned or private businesses. For example, they too often seize homes or farmland for commercial development with little or no compensation for those they displace, let construction companies shortchange transient workers, or award lucrative contracts to allies in return for kickbacks. This helps produce perhaps two hundred thousand of what the state calls “mass incidents” each year—local protests often squelched by thugs, either in or out of police uniform.

Late last month, Control Risks, a consulting firm, told business travelers to be extra careful when visiting Guangzhou, the largest city in southern China. Residents of one suburb clashed with police over government plans to demolish their homes, alleging they were offered inadequate compensation due to collusion between officials and developers. “Avoid all demonstrations to mitigate the incidental risk of exposure to violence,” Control Risks warned its clients. It said a similar case in Guizhou province three weeks earlier brought a tear gas response and the arrest of several protesters who had overturned police cars and blocked roads.

The general public, broadly aware of all this thanks to social media and the Internet, is increasingly upset. Citizens have no effective political channel for seeking redress—determined protesters can wind up in labor camps or illegal “black jails” without trial—but the regime is well aware of the potential danger; President Xi and others have warned public disaffection may erode the party’s political authority, just as it has already undermined moral authority. The fact that many Chinese, for good reason, consider the air, water and food to be unsafe adds to the sour mood.

In recent decades, Beijing has bought off much dissent by trading ever-rising incomes for political passivity. But there are doubts about how much longer that bargain can be sustained. The economic growth rate has slipped below 8 percent (still startling by global standards) and a years-old promise to expand the economy’s consumer sector so far isn’t succeeding. Last year, in fact, the investment share of the total economy increased slightly while the consumer sector shrank a bit in 2013’s early months—the opposite of declared policy. Various statistical measures suggest the growth rate is continuing to fall.

Expanded and more balanced economic relations between the $8.3 trillion Chinese economy and the $15.7 trillion U.S. economy would help both nations, but major obstacles remain. China wants continued access to the U.S. market, where political demands for limits continue to simmer—on solar panels, for example. It also wants to buy certain American technologies, now restricted by Washington because some could have military applications. (European suppliers ship dual-use items more freely.) Beijing also claims to want continued American and other foreign investment, but U.S. companies complain protection-minded bureaucrats tilt the playing field against them.

For years, the United States has complained that China costs American companies billions because it won’t curtail the theft of intellectual property; Beijing keeps promising to crack down even as some of its own departments continue to use pirated software. American exporters also complain that business regulations such as product-safety standards sometimes exclude their goods—though the same rules apply to Chinese companies haphazardly at best. This is not always by design; the central government’s enforcement mechanism is weak and its decrees are often ignored in the provinces. Having to deal with corrupt officials is another recurring business complaint. Washington also wants Beijing to move faster toward having a convertible currency, increasing imports and opening its financial and services markets.

Some of this may be coming. Premier Li Keqiang, who oversees the economy, recently cited current unfavorable statistics and said, “we need to rely upon the market mechanism” and “get rid of controls which are not needed.” He also ruled out costly new stimulus packages. “The market is the creator of social wealth,” the Communist Party’s number-two man explained. “It’s the internal source of economic development” while more “foreign investment also has potential.” If President Xi convinces President Obama that attitude will shape future policy, many economic differences could be resolved.

But finding common ground on security issues will be more difficult and could hinder consensus about overall relations.

A blustery Chinese nationalism is part of the problem for both other Asian nations and the United States—and at times for Xi himself. China’s nineteenth- and early twentieth-century history combines regime failures and victimization by outsiders; the country that once considered itself the center of civilization became a weak entity ripe for exploitation. Ever since, especially when Mao’s ideology held sway, China has had trouble adjusting to more normal relations with other countries. At times, this has helped foster a chauvinism that Beijing leaders alternately encourage or suppress for political reasons. China’s top men often find it useful for rallying support but worry that an emotional nationalism might get out of control.

These days, revived nationalism causes Beijing to assert ownership over uninhabited islands held by Japan since 1895, and make seemingly absurd claims over much of the South China Sea, including a reef near faraway Brunei that lies sixty feet deep. (Chinese ships come by occasionally to toss official markers overboard.) One result is a recurring display of military brinkmanship involving Chinese ships and planes, and those of Japan, Vietnam and the Philippines—and creates Asia-wide worries about Chinese intentions. There are fears that unwanted violence could result if someone’s pilot or gunner becomes overly aggressive.