I think that part of the reason for a lack of protest from the left is the fact that the war has dragged on for so long. I'm not on the left so I can't speak directly for them, but I'm sure there are also a lot who support President Obama and have muted their protest as a result.
However, we're now more than seven years removed from the beginning of the Iraq War and almost nine from the beginning of the Afghan war. I'm not aware of any quantifiable data to back this assertion up, but I suspect that the natural tendency is to go apeshit protesting as the war starts, then things cool off as the reality of the war sets in (assuming that our soldiers aren't getting annhilated), then as the war prolongs more protesting will begin to occur again. This all assumes that the war is not going overwhelmingly well for them of course.
Now this basic pattern will ebb and flow depending on whether or not a Dem is in power since a large majority of protesters seem to be left-wing or at least left-leaning. But I think that unless tangible proof of increased success appears, the left will begin to rally against Obama, especially if he happens to get re-elected. The left will probably start to make a little bit of noise pretty soon, but it'll be little more than lip-service from the hardcore anti-war and then they'll quiet down once election season rolls around so as not to harm Obama's campaign. Were a Republican to win and not pull out or were the war to continue at a stagnant pace, the left will go apeshit once again. If Obama wins again, this MIGHT happen toward the end of his second term, but most likely it won't. I suppose at that point whoever the next candidates are will have an impact on the level of protesting as well.
But regarding the possibility of the right starting to protest against the war, especially if Obama is re-elected, I don't see it happening in large numbers. If the wars were to continue with Obama the right would probably have a larger issue with HOW Obama handles it rather than whether we should simply be there or not. But there's never really been a whole lot of protesting over how a war is run, from either side, but rather over whether or not the war should even exist.
But I think it's definitely a possibility that the left will begin to protest to some sort of degree if the wars continue to creep along even if Obama is in office. Although LBJ had a much lower level of popularity amongst the left than Obama does, the left went pretty nuts while he was in office over the Vietnam War. I don't know if we'll ever see that level of sustained protest ever again though. We'll probably see a delayed but somewhat significant level of protest. It won't be as loud as if a Repub were to win but naturally the left is going to give their guy more slack than the other guy. The same holds true for the right.