assad is aligned with iran, US saw an oppertunity to get rid of a link between iran and hezbollah and gain another "ally" in the ME.

this effort was a failure and have become less important as iranian and us relations have become better with the nuclear deal. the islamist rebels turned to AQ pretty early(with constent and encouragement from gulf monarchies, they want to weaken iran and spread their ideology) and has made it impossible for the US to support. the few rebel groups that didnt lean on AQ have a hard time becuase of their numbers(rebels mostly sunni islamists). now the islamists is facing the consequence of the choice to lean on aq and they dont like it. queue the US is evil hype train.

iran, hezbollah and russia have all supported the syrian goverment from the start. syria has been a long time ally to all three.

turkeys involvement is mostly about the kurds and the turkmen that live in syria. if turkey sends troops, KSA would have massive difficulties doing it, the US might have to get involved even against their wishes.

US has successful partnership with the kurds and they are not openly hostile to the syrian goverment. this kurdish lead group also have good relations with the russians. this is what i believe the us hopes for, syrian goverment and kurd led negotiated peace deal after driving out the islamists. now turkey is threating the us to choose between this group and turkey. any open support of turkish invasion would be more or less an attack on russia. same with bombings of saa frontlines, russian advisors would be targeted. only russia, iran and hezbollah has the offical sanction of the goverment in syria to be there, all other activity is technically illegal. also keep in mind that NATO act 5 cant be invoked by turkey since theyre the aggressor.

dont know if it makes sense but ive tried my best.