Maybe it's just one air strike. What if it isn't? These things escalate. Others are better equipped than I am to handle the tactical side, so here's some political science.
Trump is a public opinion disaster. Gallup hasn't had him above 50%, ever, and lately, they've had him south of 40. Wars boost public approval of the president, right? We even have a buzz-word, for it, right?
The "rally-round-the-flag" effect. When there are international crises, approval of the president tends to go up. Tends. Why the wishiwashiness of that statement? It is conditional. Everything is about party identification (the one point I know my students will remember, years later). Most people don't have well-defined belief systems, particularly about foreign affairs. So, they'll take signals from trusted partisan elites. That makes public opinion dependent on elite signals.
The key reference here is Richard Brody's Assessing the President. When elites rally around the president, so do the great unwashed masses. Seriously, people, take a fucking shower. And use some better soap. Some deodorant wouldn't hurt either.
Anywho, who are these elites anyway? Members of Congress, media figures, that type of person. If they decide that we all need to get in line behind Trump, then the unshowered masses will unthinkingly do so because they don't have well-defined opinions about what do do in Syria.
The trouble is that elites are strategically constrained. If they think that they need to get in line to avoid ostracism, they will do so. It's a sort of collective action problem. Nobody wants to be the one person who won't get in line, unless they represent Berkeley (Barbara Lee opposed going into Afghanistan after 9/11, and was the only one in Congress to do so). If this goes past an air strike, what will Democratic politicians and other elites do? We'll see.
But seriously, bathe.