Once the first candybar comes out, we become confused and so do the friggin natives.
I would say, maybe the Senate, yes, yes and it's too early to tell.
The only important "enemy" in this equation would be public opinion. Once support for the mission goes away, our chances of success plummet to near zero. Unfortunately, the lesser enemies you cite know this all too well, and would invest all their time and energy into turning public opinion against the Administration. A nation's leaders cannot make these considerations the make or break conditions for engaging in action, as you correctly point out, but they certainly cannot totally dismiss them either.
With the 9/11 attacks and Saddam, the actions in Afghanistan and Iraq pretty much sold themselves. The public didn't need much convincing that these were worthwhile jobs to undertake. Liberia is going to be a much harder sell, and as a result public support will be much more fragile.