Active volcanism observed on Io is thought to be driven by the temporally periodic, spatially differential projection of Jupiter's gravitational field over the moon. Previous theoretical estimates of the tidal heat have all treated Io as essentially a solid, with fluids addressed only through adjustment of rheological parameters rather than through appropriate extension of the dynamics. These previous estimates of the tidal response and associated heat generation on Io are therefore incomplete and possibly erroneous because dynamical aspects of the fluid behavior are not permitted in the modeling approach. Here we address this by modeling the partial-melt asthenosphere as a global layer of fluid governed by the Laplace Tidal Equations. Solutions for the tidal response are then compared with solutions obtained following the traditional solid-material approach. It is found that the tidal heat in the solid can match that of the average observed heat flux (nominally 2.25 W m-2), though only over a very restricted range of plausible parameters, and that the distribution of the solid tidal heat flux cannot readily explain a longitudinal shift in the observed (inferred) low-latitude heat fluxes. The tidal heat in the fluid reaches that observed over a wider range of plausible parameters, and can also readily provide the longitudinal offset. Finally, expected feedbacks and coupling between the solid/fluid tides are discussed. Most broadly, the results suggest that both solid and fluid tidal-response estimates must be considered in exoplanet studies, particularly where orbital migration under tidal dissipation is addressed.