The early statements and reporting on all three counts are not encouraging. And I can almost guarantee that the next couple of weeks of presidential approval polls will not remain below 40%. Turn on any cable network right now and you'll be treated to salivating responses from the likes of Rubio, McCain, Graham, and virtually every media talking heads.
Unless we see continuing military action, this'll be out of the headlines after the Sunday morning news-of-the-week shows. It might bump him a point or two up in the polls, but it'll be a temporary bump.
If we get more action, then being dragged into yet another war will prove a drag on Trump. I'd like to think that even Trump realizes that and will seek to avoid that for that reason alone even tho there are other reasons less personally applicable to avoid a war with Assad.
It won't have any kind of long term impact unless mission creep sets in and it becomes a protracted quagmire. After all, how much impact did the Kosovo Intervention or the airstrikes on Sudan and Afghanistan in 1998 or the various actions to enforce the No-Fly Zone against Iraq during that timeframe have on the 2000 Election? Add to that nowadays, the news cycle moves and turns over much more quickly, so these types of events have even less impact. Recall that the Syrian government's earlier chemical attack back in 2013 was washed out of the news cycle within a few days by Miley Cyrus twerking at the VMAs.
However, to the original post, for now, a limited, proportional retaliation is justified. The real danger here is mission creep, that the U.S. gets dragged ever further into the Syrian Civil War. Now, the same risk would exist under President Obama, President Clinton, or President Bush, Rubio, or Cruz, but Trump is uniquely poorly placed to handle it: his staff is riven by internal dissent, he is an amateur who delegates to other amateurs rather than experienced advisors, has no experience with foreign policy or knowledge of how statecraft works, and worst of all, he seems to be influenced by whoever he spoke to last.