Even if there is no intervention by the US, a Chinese invasion of even Quemoy or Matsu would cause serious economic disruption in the Chinese stock market, people thrown out of work and other problems. The rulers of China know that as long as they can maintain a healthy growth rate, public dissent will not cause them serious problems. Any military action would impair that growth rate.
China plans to peacefully integrate Taiwan in the same way it has been dealing with Macau and Hong Kong. One of the two major parties of Taiwan. the Kuomintang, also maintains that Taiwan is a part of China. The US officially also recognizes Taiwan to be a part of China and not an independent country.
China and Taiwan just disagree on the terms. Taiwan is quite similar in many ways to the prosperous coastal part of the PRC. Everyone speaks Mandarin (not the case even in Macau or Hong Kong), and the government acknowledges the influence of Confucius, who is increasingly becoming philosophically more of a national mentor hero than Mao.
Taiwan has a GDP of over five times that of mainland China. The Taiwanese do not want to be flooded by Chinese immigrants, nor do they want their standard of living to decline. The PRC does not want this, either. Immigration from mainland China to both Macau and Hong Kong is seriously restricted.
