Using constrained simulations of the local Universe for generic cold dark matter and for 1keV warm dark matter, we investigate the difference in the abundance of dark matter halos in the local environment. We find that the mass function within 20 Mpc/h of the Local Group is ~2 times larger than the universal mass function in the 10^9-10^13 M_odot/h mass range. Imposing the field of view of the on-going HI blind survey ALFALFA in our simulations, we predict that the velocity function in the Virgo-direction region exceeds the universal velocity function by a factor of 3. Furthermore, employing a scheme to translate the halo velocity function into a galaxy velocity function, we compare the simulation results with a sample of galaxies from the early catalog release of ALFALFA. We find that our simulations are able to reproduce the velocity function in the 80-300 km/s velocity range, having a value ~10 times larger than the universal velocity function in the Virgo-direction region. In the low velocity regime, 35-80 km/s, the warm dark matter simulation reproduces the observed flattening of the velocity function. On the contrary, the simulation with cold dark matter predicts a steep rise in the velocity function towards lower velocities; for V_max=35 km/s, it forecasts ~10 times more sources than the ones observed. If confirmed by the complete ALFALFA survey, our results indicate a potential problem for the cold dark matter paradigm or for the conventional assumptions about energetic feedback in dwarf galaxies.