There are a bunch of things out there that I suspect I'm going to write about with respect to Barack Obama, presidential power, presidential reputation, and Syria...I'll start with what might seem the most obvious, but a point that isn't being made much and should be.
The preface: There are multiple balls in the air. There's the effects of winning vs. losing a Congressional vote. There's the effects of forcing a Congressional vote, which Obama did, as opposed to not forcing it, which is what everyone expect. But then there's also the effects of actually carrying out the policy (that is, a military intervention) or not. And that last one has all sorts of possibilities, right? The scale and scope of the intervention could be various different sizes and durations, and could go well or badly; some of that is within the control of the White House, and some isn't.
Of all of those, there's one permutation that absolutely, no question about it, would destroy the rest of Barack Obama's presidency is: a disastrous war. Ask Lyndon Johnson or George W. Bush. Or Harry Truman. Unending, seemingly pointless wars are the one sure way to ruin a presidency.
Now, I'm not saying that's in the cards; in fact, I don't think it is. I'm just saying: that's the kind of thing that really does matter a lot to presidencies. And if you do believe that the administration is going down a path that winds up there, or a path that has a high risk of winding up there, then you should be very worried about the health of this presidency.
If not? None of the other permutations here are anywhere close to that kind of threat to the Obama presidency. Presidents lose key votes which are then mostly forgotten all the time. They pursue policies which poll badly, but are then mostly forgotten, all the time. There are important things to say about all of that, because "mostly" isn't completely. But the first thing to get right when considering the effects of Syria policy on the rest of the Obama presidency is that the scale of a Vietnam or an Iraq (or a Korea, for that matter) overwhelms everything else we might talk about.