It is shown that the homogeneous spiral state of the doped Hubbard model is unstable for infinitesimal doping concentration. The spin response about the Hartree-Fock spiral state is evaluated, considering both the interband and intraband processes. Driven by long-wavelength, intraband spin fluctuations, the instability towards infinitesimal fluctuations about the mean-field state is inferred from the nature of the static spin response.