The Cassini Plasma Spectrometer has reported dramatic perturbations of the magnetospheric plasma flow in a region extending at least 30 satellite radii away from Saturn's small but active icy satellite Enceladus. We interpret these observations here by means of a steady state model of the electrodynamic coupling between Enceladus and Saturn. Neutral water molecules from Enceladus are ionized, predominantly by charge exchange with ambient ions, to produce a pickup current that accelerates them to the local plasma velocity. The consequent addition of angular momentum requires Birkeland (magnetic field-aligned) currents that couple the newly injected plasma to distant parts of the flux tube and ultimately to Saturn's ionosphere. The rate of local ionization in our model varies with the inverse square of distance from the satellite and is scaled by a free parameter proportional to the ratio of the total mass-loading rate to Saturn's ionospheric Pedersen conductance. To explain the observed velocity perturbations, we require a total mass-loading rate $gtrsim$100 kg/s if the conductance is $gtrsim$0.1 S as expected. If the mass-loading region is not strongly coupled to Saturn's ionosphere, then the appropriate conductance is the Alfv¿n "wing" conductance ~2 S, requiring more than an order of magnitude more mass loading. In either case, Enceladus is clearly implicated as a significant, if not dominant, source of Saturn's magnetospheric plasma.