Americans will likely judge the war in Iraq as a failure?
If the new government holds after we withdraw most of our troops the war will be seen at worst as "ill advised" based on the cost in treasure and lives. I suspect that the war will be given a small margin of public approval under those circumstances.
Since public opinion will probably be shaped by spin in the short run, the real answer will be left to the historians twenty or so years out. If Iraq become the paragon moderate Islamic state, it will be hard to say the war was anything but a good thing for the world, regardless of it's impact on our taxpayers.