The Realpolitik here is probably more important than any abstract concepts. And that points to the US not being overly involved for a while yet.
For starters, what are American interests here? Arguably the greatest benefit the US can have is to keep Syria unstable and off the world stage. Assad regaining control would re-enforce the Iran-Syria-Hezbollah opposition to Israel, which indirectly hurts the US by forcing greater support of an ever more hostile Israel. On the other hand the rebels hardly look likely to support the US if they did gain control. Maybe if there was earlier and deeper involvement, but even then it was a long shot. The US trying to swing a victory where some ally comes into power seems incredibly unlikely from here.
So then we have humanitarian concerns. Obviously there are fog-of-war problems determining when whatever lines you choose have been crossed which, in Syria and with active disinformation on both sides, pretty much makes the go/no-go call entirely arbitrary and hard to defend. Further, there is no international modern doctrine of pre-emptive engagement to prevent humanitarian problems. The closest we have ever come was the UN resolution against Libya which called for UN authorised forces to use force in the protection of civilians. That resolution is now seen as a strategic error by both Russia and China and I don't see anything like it passing in the near future. And unilateral action on the part of the US seems even less likely right now, especially if it is flying in the face of other major powers (in this case, Russia) or the UN.
But imagine that world opinion did swing all the way and the UN authorised an intervention. What would any intervention look like? I'm going to take it as read that there is no scenario where the US is going to invade. Boots on the ground look unlikely at best. Any such intervention would be - as a maximum engagement level - along the lines of the Libyan one; an actively maintained no-fly zone combined with (mostly distant) air support of rebel forces. Except, even leaving out that last bit, such an engagement would be far more substantial than was involved in Libya.
Syria has a substantial air-defence network. While it can be penetrated (as Israel proved)
establishing a no-fly zone would be far more involved. You effectively have to destroy their entire air and anti-air capability, then maintain that control for as long as the zone needs to be maintained. Given the quality of Syria's defences you would be talking hundreds of airstrikes and missions, very likely involving lost American aircraft and crew. It would be closer to the effort the Air Force put into the initial invasion of Iraq than the efforts over Libya, especially if it were a unilateral or bilateral (with Israel) effort. The cost would be obscene, even before looking at how it would distract from other ongoing American operations and readiness in other theatres.