Organized electricity markets often require submission of supply functions ahead of the realization of uncertain demand. As a model of oligopoly behavior, the Nash condition of supply function equilibrium has a natural appeal. Typically this produces a continuum of possible equilibria, presenting an equilibrium selection problem. Beyond existence, stability of an equilibrium would be an obvious criterion for selection. For affine demand and marginal costs, polynomial approximation provides an approach for analyzing the stability of unconstrained supply function equilibria. The set of stable approximation equilibria is small and its properties suggest that the set of stable exact supply function equilibria is empty.