If I could predict the economic future I wouldn't be posting here right now. But there's basically two points of view on this.

The first one recalls that Japan followed a very similar development trajectory, only to implode in the late 1980s. This argument holds that China's recent rise is temporary and the US has nothing to worry about -- similar to what happened after Japan collapsed, the US will resume its predominant position in the order of things.

The second one notes that China's government so far appears to be managing its economic rise quite well, and more importantly has a lot more people to draw on, so its manufacturing advantage in terms of labor costs could potentially last a lot longer than Japan's did. Based strictly population, China would have four times the GDP of the US by the time its GDP/capita (a rough proxy for labor cost) equals the US. This means this situation could last for decades. Whether this is harmful or not is really a matter of how you view China's intentions. If they played according to WTO rules, there's no economic reason why we couldn't keep producing services (financial and otherwise) and trading them with China for goods. The problem, of course, is China hasn't always obeyed WTO rules in the past.

A longer-term POV, of course, would note that third countries -- India, Vietnam, Malaysia, etc. -- are also rising to compete with even lower labor costs, which suggests there may be no opening in the forest anytime soon. Of course, this isn't necessarily a bad thing -- it does mean that billions of people are being pulled out of poverty.

Historically, production in China was cheaper due to lower labor (and land) costs, so over the decades many companies moved labor-intensive manufacturing operations there. In turn, this meant other countries had to start importing these goods from China, resulting in a balance-of-payments deficit. As a result of this China now has a large share of the world's manufacturing base, as well as large foreign currency reserves that can be used to buy goods/land/resources/companies abroad. China has historically used many of these reserves to buy hundreds of billions of dollars worth of US Treasury Bills, so in theory the US is legally indebted to China. Two things to keep in mind though: 1) China's lower labor costs won't last -- they're rising at 15-25%/year. As a result many companies have already begun shifting manufacturing operations back out of China, this time to even lower-cost manufacturing countries like Vietnam, Malaysia, Burma, etc. 2) China can't really use its US Treasury holdings to bully the US -- in fact, it can't even really count on the value of all the US Treasury Bills it holds. If it starts dumping US Treasuries in bulk, the price of treasuries will drop like a stone and wipe out much of the value of China's foreign reserve. Moreover, US Treasuries are, in the end, just a promise from the US government to pay with no real guarantee -- if China starts using them as a weapon, the US may just opt to repudiate the debt (though not without major consequences in terms of investor confidence and future interest rates).

The Chinese government would hurt more. Since Deng Xiaoping the CCP's legitimacy has come almost entirely from its ability to bring continued economic growth to its citizens, and that economic growth is in turn based almost entirely on its export economy. See, for example, the mass unemployment, bankruptcies, and economic disorder that hit the manufacturing-and-export-heavy Guangdong Province with the onset of the global economic crisis in 2008. One thing is for sure: the Chinese government would do everything in its power to keep a repeat of that from happening.

Or more likely, Japan will just shift its neodymium orders to mines in the US, Australia, Brazil, and elsewhere, as these will increase their output when China drives up global prices by restricting her exports. Rare earth metals are only relatively rare -- we're not nearly about to run out of the things, and China isn't the only country with significant total reserves. At any rate, Japan doesn't owe China war reparations anymore anyway: Mao Zedong waived all reparations as part of the price for buying Japan's diplomatic recognition in 1972.

With the exception of Vietnam, they're all pretty consolidated democracies...