Polls on that very topic are a regular part of election cycles in Taiwan. Back in the late 80s there was a sizable minority of Taiwanese people identified themselves as Chinese and many others identified as Chinese and Taiwanese.

Now about 2/3 of the population identifies as Taiwanese, about 1/3 identifies as Taiwanese and Chinese and the percentage identifying as Chinese is less than the standard error of the surveys. The long term trend shows no sign of slowing down or reversing either.

If you're interested in the topic, Zhengda (aka NCCU) has an election study center and publishes their findings.