I tend to be more practical.
Could we save lives if we intervened in Syria? Yeah, probably. Should we? No. The interests of the United States are not served by trying to save lives around the globe.
Decision consequences:
1. If we intervene, and fail, we will appear weak.
2. If we intervene, and succeed, we will be hated by most of the new regime. Many of them are virulently anti-U.S. now, and historically, aiding or encouraging rebel movements in the Middle East has not worked out for us. Moreover, rebellions tend to put more ideologically motivated and radical people into power, as opposed to people who simply want to maintain power. The radical line in the Middle East is a radically anti-American one.
3. If we do not intervene, and Assad loses, we will likely face the same situation as 2, but with the rebels weakened by losses. Syria will be a weaker state, and we will have spent no blood or treasure.
4. If we do not intervene, and Assad wins, we will have a weakened authoritarian state that will be unlikely to court further hostilities with us, and we will have lost nothing.
In terms of international relations, we are going to be blamed for whatever happens. If we intervene, the international media will happily criticize us for aiding terrorists, plaster pictures of the results of every errant bomb or collateral damage event, and we will generally be tarred with the "aggressive, warmongering" brush. If we do not intervene, we will be considered selfish, arrogant, blind to the suffering of others, etc. However, in the latter event, the United States will not have spent dollars and lives on protecting people whose safety and happiness brings us no advantage.
Therefore, the best approach for the United States is to let the Syrians kill each other until one side or another achieves victory, or it becomes a failed state. Either way, it's not our problem. If anything, it's the Israeli's problem, and they get enough aid from us to where they should pull their own weight if necessary.
P.S. Actually, considering the fact that both sides in Syria are likely to remain our enemies, from a - purely - pragmatic approach, we should attempt to prolong the fighting as long as is possible, so that the final result is a state too weakened to pose any sort of threat to its neighbors, or to provide any sort of aid to other of our enemies.