Taiwan would lose half its population and China less than .1% in such a war. Taiwan would lose its economy, China less than .1%. Is Taiwan really going to oppose the invasion? Is dead better than red?
An independent Taiwan represents a major competitor to China. An annexed Taiwan represents an important increase in industrial, research and military capacity and a vital location for expansion in the Pacific.
North Korea and China can easily invade South Korea. Is the average AMerican willing to go to war against both contries to save South Korea?
Clinton sent 2 carriers at a time when America was much stronger and China much weaker, two decades later it is doubtful that Obama would be allowed to do the same and that China would pay any attention to the carriers (being there doesn't mean they will attack, starting WW III over a small island).
Blockades were going to suffocate Napoleon, Germany in WW II, etc, but they didn't.
In Napoleon's era there was no connected global economy. Germany's economy was war-oriented and China is totally dependent on global exports. More than half its oil must be imported and it's sea routes easily blocked.
When China invades Taiwan and South Korea (which they will not do) it's economy will collapse.
China is for the moment more occupied with its internal affairs. The political leadership is scared to death for a "chinese spring". Many wrong internal investments were made and the families of the top businessmen are already leaving China.