We can't bomb the chemical weapons stockpiles because doing so would release them and kill thousands or tens of thousands of civilians. It's not like taking out a SAM site.
At the same time, an aerial bombing campaign to support the rebels WOULD trigger a chemical launch, because Assad has already made it clear that they would be used if the country was attacked from the outside.
Sending in a large ground force to seize the sites is the only way to pull it off. That would probably trigger a chemical weapons attack itself, but our forces have the gear to survive it (there would undoubtably be civilians nearby who were killed too though...the western part of Syria is fairly heavily populated).
The problem with sending in a large ground force is the fact that Assad still has a fairly substantial and well trained army with modern weapons. Syria isn't Iraq, where the army had already been decimated by another war and a decade of sanctions, and it isn't Afghanistan, where there wasn't a well trained army of any sort. It has a large regular army equipped with the best weapons the Russians would sell them. I have ZERO doubt that the U.S. military would slaughter them in combat, but we'd probably still be looking at an American death toll higher than that of Afghanistan and Iraq combined. The fight would be short but incredibly brutal.