I see very little benefit to the US in making any sort of military strike against Syria. Unfortunately, following the same flawed "Domino Theory"* that was our driving principle during the Cold War and got us involved in Vietnam, I also see the same pieces of the board moving into position to make a military strike.
The argument will go something like this I imagine: Within the Middle East, Iran is the largest supporter for Syria and the Assad government. This support comes through direct aid as well as through the terrorist group Hezbollah, as well as other similar groups. Weakening Assad by proxy weakens Iran.
To me though, the argument falls flat because even if Assad is removed from power Iran is still in a better position than the US to influence the next leadership of the country, whatever shape it takes. Or conversely, since I believe Syria is like most of the rest of the Middle East and predominately Sunni in population (as opposed to Iraq and Iran, which are majority Shiite) then the new government will be influenced by the likes of Saudi Arabia. Either way, we spend millions or more likely billions of dollars we don't have and gain...what precisely from that expenditure?
I also think it's a bit hypocritical on the part of our government to condemn any sort of chemical weapons use, when released CIA documents
shows we were accessories to the largest use of chemical weapons post World War I.*The Domino Theory was the idea that if one country fell to communism, then it would set up a chain reaction where all its neighbors would become communist as well.