The Republic of China is a problem that the People's Republic of China government has tried to resolve since its inception in 1949. On the other hand, the People's Republic of China is a problem the Republic of China government has tried to resolve since its inception in 1949. The relationship between the two entities has varied wildly in the past 57 years, edging occasionally towards conflict and the brink of war.
Taiwan has been an incredibly complex issue for the United States, as well. From 1949 to 1971, the United States backed the Republic of China (run by the exile KMT government on Taiwan) as the legitimate government of all of China. In the 1950's and 60's, The People's Republic (headed by the CCP on the mainland) made moves towards war, using backyard iron works to produce shells designed to fly over the strait. China lacked the military material and technology to mount an offensive, but was able to solidify its threats when it tested atomic and thermonuclear bombs.
In 1971, the United States and China turned fully around. Nixon and Kissinger's various envoys to China brought recognition from the United States of the CCP as the legitimate government of all of China, and new diplomacy and trade. (Contrary to the belief of many, the United States does not officially recognize the KMT government.)The United States insisted that China's resolution with Taiwan be "peaceful," and it would not allow war. China and the US grew closer, but strains over Taiwan remained.
In the 1990's, strains over Taiwan became crises. In 1994, the Republican-majority congress put pressure on the Clinton administration to take Taiwan-friendly steps, including allowing a visit from its prime minister. In 1996 and 1998, China put forth aggressive confrontational efforts to intimidate Taiwan, firing missiles into the oceans near Taiwan's largest port cities, causing panic and economic recession. The United States twice responded by sending aircraft carrier fleets to Taiwan to assert its dedication to maintaining peaceful relations across the strait.
The People's Republic of China's policy firmly remains that Taiwan is rightfully a region of China, and that the Republic of China government of Taiwan is in exile. All but a few of the world's countries explicitly recognize the People's Republic and not the Republic of China as the legitimate ruler of China, and do not hold official diplomatic ties with Taiwan. The People's Republic has touted "one country, two systems" as a peaceful method of reuniting the two states.
Understandably, many Taiwanese are not particularly enthusiastic about the idea. The pan-green coalition currently rules Taiwan, and strongly leads towards eventually making Taiwan an independent state. Although Washington does not publicly support the idea, and Beijing has threatened invasion on multiple accounts if Taiwan were to declare indepdendence, Taiwan may have a brief window where the PRC's power position is weak.
Beijing, in striving for modernity, has sought the acceptance of the international community into great power status. Its most recent great symbol of modernity shall be the 2008 Olympics, held in Beijing. To this end, the PRC has striven to impress the international community by pouring resources into cleaning up public streets, fixing bad English on signs, etc. Statues and heavy internal advertising, touting the coming Olympic games, are all over the country. The People's Republic sees the successful operation of the 2008 Olympics to be a great symbol of China's vaulting into modernity. Anything to either hinder these Olympics or undermine the good press to come from them would likely be avoided if at all possible. The Chinese, therefore, are going to be very wary about making military action against Taiwan as those Olympics approach.
Knowing this, the Taiwanese politicians may be mulling a possible independence bid. To make matters more interesting, Taiwanese elections will likely be held in early 2008 (the Taiwanese do not set the date until late), and President Chen is a lame-duck. As such, he has some freedom to make possibly controversial measures, and he already has in the past. In 2006, he disbanded the Reunification Committee in Taiwan, symbolizing his lack of dedication in reunification. China was infuriated, but could do little in reaction. A bold Chen may try to set up Taiwan for independence before his term is done.
At the same time, US President George Bush is a late lame-duck, as well. Should Taiwan declare independence, he has the US Pacific Fleet (complete with 2 active aircraft carrier groups) to move to Taiwan and enforce its sovereignty, should he need to. His politics largely hail from the 1990's Republicans that spent many years pressuring the Clinton administration towards diplomatically friendly measures with Taiwan (like allowing the Prime Minister of the ROC to visit), and his style of "Cowboy Diplomacy" makes him unlikely to be too hesitant about deploying the US Navy to accomplish his diplomatic goals. Knowing Bush is on the way out (and suspecting a more militarily restrained executive might follow), the ROC may very well want to take advantage of his diplomatic style.
The chance that Taiwan will declare independence remains low. But parallel events are making the chance that it might happen, and work, more likely. As much as the People's Republic of China may be furious at the idea of an independent Taiwan, US help would put China in a tough place. A direct conflict with the United States would halt critical exports, and would likely bring harsh criticism of the international community. It is this, along with the PRC's deep need for international approval, that is most likely to make them helpless.