Motivated by experimental evidence for the importance of fermionic deg
rees of freedom near the superconductor-insulator transition, we take
into account gapless electronic excitations for the description of the
transition. Integrating them out yields a damping for the phase of th
e superconducting grains. We derive a Ginzburg-Landau-Wilson descripti
on for the onset of superfluidity which shows a non-ohmic dynamics. Th
is dynamics depends qualitatively on the strength of the damping. Suff
iciently strong damping modifies both, the critical behavior and the r
esponse near the transition. The critical exponents depend on the damp
ing strength. The conductivity at the transition is finite but non-uni
versal.