The fundamental question of committing U.S. troops, treasure and ordnance to a strike on another nation first rotates around "what does the U.S. get out of the deal?"
As far as I can tell there is nothing more for the U.S. to gain by striking Syria than expressing moral outrage in the most hideously expensive way possible with the secondary benefit of distracting the American public from the many and vast failures in domestic policies and assaults upon the Constitution generally and civil rights specifically by an administration composed of Chicago machine thugs and knuckle-draggers.
There is, however, quite a bit to lose.
Both Syria and Iran have threatened that "Israel will Burn" should they be struck - and both rogue nations are demonstrably crazy enough to engage in such a strategic mis-step. The fatal error in strategic assessment is to forget the Israelis have been surrounded by hostiles for a very long time - and have long hinted (rather unsubtly) at a "Samson Option," - a re-enactment of Masada on a far grander and more high-tech scale.
Under this last-ditch option, if Israels leaders believe the nation is either about to be destroyed or is actually destroyed - Israel would then launch its 250+ nuclear warheads not only on its neighbors in the Middle East, but on nations world-wide in the ultimate "nothing left to lose" move.
It seems unreasonable to expect the targeted nations to exercise vast restraint at that point. More likely, the phrase of the day will be "let the fun begin."
All this would tend to weigh against intervention in Syria, even before we look at the question of whether it is the job of the United States to play "Policeman of the World." Or the question of whether the President has the authority to engage in Acts of War without either a declaration of war passed by Congress or some identifiable party committing an act of war against the United States (which, oddly, Syria has not).
Past Presidents have waged war as a treaty obligation, a marginally acceptable maneuver. Further, some Presidents have hidden behind the fig leaf of a "police action" ("No, really - it's not a war! We're only blowing up a few things and killing a few people!").
The current Chicagoan In Chief only grudgingly acknowledges Constitutional limits at all, and in this instance claims that in a moment of graciousness he is asking Congress before engaging in military action - but that he has the authority to go ahead and strike where and when he wants in the face of either Congress failing to approve such action or in defiance of Congressional action actively forbidding such action.
Finally, we return to asking "why?" Syria, at this distance, appears to be suffering scumbag v. scumbag in a contest of Al-Queda supported rebels taking on a terrorist supporting and generally vile regime - with a less than entirely innocent population trapped between the warring parties.
This seems more like a situation to bring production back online and air-drop a vast number of Liberator pistols into the region than for the U.S. to engage in military intervention, thus allowing the local population a reasonable chance to work it all out for themselves. Or, perhaps, if all the stars line up to make it possible to exterminate the entire leadership of both warring parties in the dark of some particularly frenzied night if some sort of intervention is found absolutely necessary.
But no, I can't say this is worth a risk of a third World War complete with smoking rubble that glows in the dark.