Superconducting films of amorphous Indium Oxide (a:InO) undergo a transition to insulation upon increasing disorder, driven by the localization of preformed Cooper pairs. The continuous decrease of the critical temperature as the critical disorder approaches indicates a similarly continuous suppression of the superfluid density. In this talk I discuss the fate of the superfluid density in the vicinity of this transition to insulation. We have accurately measured the superfluid density by a systematic study of the plasmon dispersion spectrum of microwave resonators made of a:InO, combined with DC resistivity measurements, as a function of disorder. We observed that the superfluid stiffness defines the superconducting critical temperature over a wide range of disorder, highlighting the dominant role of phase fluctuations. Furthermore, we found that the superfluid density remains surprisingly finite at the critical disorder, indicating an unexpected first-order nature of the disorder-driven quantum phase transition to insulator.