Stick-slip behavior is a distinguishing characteristic of the flow of Whillans Ice Stream (Siple Coast, Antarctica). Distinct from stick slip on Northern Hemisphere glaciers, which is generally attributed to supraglacial melt, the behavior is thought be controlled by basal processes and by tidally induced stress. However, the connection between stick-slip behavior and flow of the ice stream on long time scales, if any, is not clear. To address this question we develop a new ice flow model capable of reproducing stick-slip cycles similar to ones observed on the Whillans Ice Plain. The model treats ice as a viscoelastic material and emulates the weakening and healing that are suggested to take place at the ice-till interface. The model results suggest the long-term ice stream flow that controls ice discharge to surrounding oceans is somewhat insensitive to certain aspects of stick-slip behavior, such as velocity magnitude during the slip phase and factors that regulate it (e.g., elastic modulus). Furthermore, it is found that factors controlling purely viscous flow, such as temperature, influence stick-slip contribution to long-term flow in much the same way. Additionally, we show that viscous ice deformation, traditionally disregarded in analysis of stick-slip behavior, has a strong effect on the timing of slip events and therefore should not be ignored in efforts to deduce bed properties from stick-slip observations.