The Tharsis rise represents the most significant long-wavelength gravity and topography anomalies on Mars. Two competing models have been proposed to explain the origin of these anomalies. In the first model the Tharsis rise is attributed to loading of volcanic construction on the lithosphere, while in the second model these anomalies are explained as dynamic effects of a one-plume thermal structure below the Tharsis rise. In this study we seek to distinguish between these two models by formulating a generalized viscoelastic loading model that determines responses to loads at different depths. With this new formulation we found that the instantaneous viscous flow loading formulation used to compute responses from a plume may significantly overestimate the geoid anomalies if the elastic thickness of the Tharsis lithosphere is ~150 km as inferred from gravity and topography data. We suggest that the one-plume structure if currently existing below the Tharsis rise may be responsible for only a small fraction (<10%) of the Tharsis geoid anomalies and that other processes, including surface loading of volcanic construction, may be the primary cause of the geoid anomalies. The plume structure is inefficient in producing geoid anomalies because the long-wavelength components of the plume structure are confined to a ~300 km layer below the lithosphere in which the geoid response is minimal. Future studies on gravity and topography at different wavelengths may put constraints on possible contribution of a plume to the elevated Tharsis topography.