What is the "Surge?"

[Schmedlap]

This definitional difference seems to be at the heart of disagreements over whether it has "worked" or not. Those disagreements go on to buttress basic policy differences.

I think you got it backwards. Politicians start from a position and then seek ways justify the position.

Is the surge something the military should provide a precise definition for (assuming there isn't one already that I've somehow missed)?

No. The positions have been staked out. All candidates will shift this way and that, but none will shift too far from where their base of support wants them to go. If the military were to attempt to clarify the definition, it would immediately be spun by both sides to rationalize some way that it bolsters their positions, making the military the unwitting tool for political nonsense (or is that a redundant term?). When objective facts are irrelevant to the outcome of an argument, it is pointless to inject them into it.