I'm not sure what a tactical strike at Syrian WMD facilities would do for the situation in that country. I'd be saying this regardless of who's in the White House.
I don't think the Assad regime is going to change tenor with a few facilities removed from service. It will make him look like the victim of a big Western bully taking sides in a civil war and might actually help his position overall.
The administration doesn't want to engineer regime change... OK. What are they after?
What they might be after is to say they did something. Diplomacy isn't all that helpful when the two factions seem to have no common ground to come to other than a common grave to bury their dead. Thus, a minimalist military action plays to the "do something" response.
It's hard to sit back and say "I don't have a dog in that fight" and let two foes go at it; it runs counter to both American do-gooderism and Christian peace-making chords in me. China-Vietnam and Iran-Iraq were two examples from my youth where the best geopolitical response was be a long, messy stalemate. That would be the realpolitik play here, a drawn-out war of attrition that weakens both the Assad-Iran-Shia axis and the jihadi-Salafist-Hamas-Muslim Brotherhood axis.
Not pretty, either way. Doing nothing empowers Assad to keep gassing the rebels. Doing a small attack makes Westerners feel good but gives Assad a high ground. Doing a big attack would either require a lengthy occupation or allowing a jihadi-state to pick up the pieces.
As the computer said at the end of War Games-"Strange game; the only winning move is not to play."