I think the big political problem is that America has wanted Assad out before chemical weapons was even an issue, and they have not deviated from that. An unpalatable political settlement might have been achievable if they were willing to let him stay in charge, meaning a lot less death overall.
So they want him gone, but to do that requires basically another Iraq. And congressman want to get re-elected. Now the Russians are involved so it's a circle that can't be squared at the minute.
Doing another Iraq would get rid of Assad, but who/what comes next? Those groups we mentioned earlier, whose interests temporarily aligned with America's may then try to fill the void (see Iraq). Many more dead, another $trillion spent and no guarantees that the situation gets any better, the reluctance to do it is logical.
The mistake, imo, was to prize regime change above everything else -- and as I say, that has nothing to do with chemical weapons, as much as they are trying to sell that as the reason.