There is no oil in Syria.
Perhaps not, but getting rid of the Assad regime would further isolate the mullahs of Iran and leave terrorist groups like Hezbollah hanging in the wind and vulnerable to Lebanon (now freed of Syrian domination) and Israel. I am sure both states would be more than happy to put Hezbollah in its place.
That is my interest in the matter -geopolitical.
Personally I am terrified of the prospect of a bosnia-type situation emerging. Supporting any one side would likely just lead to ethnic conflict on an even wider scale. Also I am not so sure that toppling the Syrian gov. would be as easy as Libya (and that obviously took a good amount of time).