Could bombing Syria kill more civilians than it saves

The answer is clearly yes, and for two reasons.

The first is that our bombs will kill people. The United States will do everything it can to minimize civilian casualties, of course. But Syrian President Bashar al-Assad won't. As James Fearon writes, "you can bet that the Assad regime will do what it can to make it so attacks do kill, or appear to kill, a lot of civilians."

The chemical attack we're punishing is thought to have killed about 1,400 people: It won't take all that many ill-targeted explosives to match that death toll.
The second — and probably larger — worry is that our bombs will lead the Syrian government to kill more people. That's the implication of this 2012 paper by Reed Wood, Jason Kathman, and Stephen Gent (which I found via Erica Chenoweth).

The authors looked at a range of conflicts from 1989 to 2005 and found that when outside governments intervene on behalf of rebel forces, the government's killing of civilians increased by 40 percent. The reason, basically, is that as the government fears it's losing control of the conflict, it becomes more desperate and more ferocious and more lethal. The authors conclude (italics mine):

    Supporting a faction's quest to vanquish its adversary may have the unintended consequence of inciting the adversary to more intense violence against the population. Thus, third parties with interests in stability should bear in mind the potential for the costly consequences of countering murderous groups. Potential interveners should heed these conclusions when designing intervention strategies and tailor their interventions to include components specifically designed to protect civilians from reprisals. Such strategies could include stationing forces within vulnerable population centers, temporarily relocating susceptible populations to safe havens that are more distant from the conflict zone, and supplying sufficient ground forces to be consistent with such policies. These actions could fulfill broader interests in societal stability in addition to interests in countering an organization on geopolitical grounds. Successful policies will thus not only counter murderous factions but will explicitly seek to protect civilian populations.

Those protective interventions are notable because they read like a list of things the United States is clearly and public saying it will not do. But that means we're considering intervening in Syria's conflict in a way that we know is likely to produce a murderous response from the government that we are not willing to stop.

The United States has been very clear that this is not a mission to save civilian lives. It's a mission to enforce international norms against the use of chemical weapons. Rather than protecting civilians from being killed, we are attempting to alter Assad's choice of weaponry when he kills them. It's entirely plausible that Assad could heed our message to stop killing civilians with chemical weapons even as he heeds his incentives to retain control of the conflict by stepping up his slaughter of civilians through more conventional means. That would, on some perverse level, be a "success" given the main goal of the policy, but it would be an awful failure on a humanitarian level.

Of course, as Charli Carpenter has written, this is not a humanitarian intervention, and Secretary of State John F. Kerry has very clearly stayed away from calling it a humanitarian intervention. But there's the awful chance that it could become an anti-humanitarian intervention.