Stemming? Not a chance. As for how long to hold out, obviously it depends mostly on how long and how effectively Taiwanese navy could contain Chinese assault. Taiwan currently has 4 destroyers, 22 frigates, and 4 subs against Chinese 26 destroyers, 52 frigates, 47 submarines (sick!), and soon they will have aircraft carriers. However, Taiwan has a pretty strong air force which could cause big troubles for the assault. If China really wants to take over Taiwan and manages to destroy substantial part of their air force very fast, thus recieving unquestionable air superiority, i'm sure it won't take more than a couple of weeks.
Geography is also Taiwan's enemy. Unfortunately for Taiwan, Taiwan Strait is just 130 km wide - within Chinese land-launched cruise missiles operational range. What's more, if you look at the map you'll see that most of cities and industry on the island is located on a tight strip of lowlands along the western coast, which means there is absolutely no room for smart mobile defense.