Calm negotation is unlikely, since both sides will believe they have all the proof they need. Both may well see the other's attitude as being extreme stubborness in the face of the obvious.
We could also add the other four countries who have staked claims (Vietnam, Malaysia, Taiwan, Brunei) - whose claims are weaker. For internal political reasons, some of these countries may wish to align themselves with one or other side or enter themselves as a separate faction.
(For the former: perhaps Taiwan might enter on the side of the Phillipines, "discovering" that the Phillipines are only claiming some x number of the islands, and that Taiwan has legal right to the remainder - the "disovery" might well be made by Phillipine researchers. For the latter, it unlikely that Malaysia would be interested in aligning themseleves with any country involved in the dispute, but it is conceivable that one of the Sultans, or a candidate for the elections may find it politically useful to incite disruption à la Argentina's General Ramos with regard to the Falklands conflict.)
Historically and psychologically, whenever the facts are unclear, emotions run the strongest. Ownership of the Spratleys is by no means clear, and we can expect any debate to be dominated by passion rather than reason. And in China we could mix in the imminent death of Deng Xiaoping, a little peasant unrest, another bad year for inflation, and perhaps some more US demands... This is a dangerous situation in which most of us are bystanders who can only wait and pray.
The most frightening consequences to me, is that it would be quite reasonable to expect other countries to be dragged into the fray if anything happens. The US certainly will be expected to take one side or another (there'll be some interesting propoganda coming from all corners!) - overseas Chinese will be demanding action, and the Phillipine government will probably request assistance.
If this does occur, it will be interesting to see Australia's reaction. It would be quite bizarre if we found ourselves opposed to the US, our most-strongly considered ally, but as it is likely that countries will join each side almost randomly, there might only be a 50-50 chance of allies "sticking together". Similarly, it is hard to imagine how the UN can avoid going the same way as the League of Nations if large numbers of its members are fighting against each other.