We compute the spectral density in the normal phase of an interacting homogenous Fermi gas using a T-matrix approximation. We fit the quasiparticle peaks of the spectral density to BCS-like dispersion relations and extract estimates of a "pseudogap" energy scale and an effective Fermi wave vector as a function of interaction strength. We find that the effective Fermi wave vector of the quasiparticles vanishes when the inverse scattering length exceeds some positive threshold. We also find that, near unitarity, the quasiparticle lifetimes, estimated from the widths of the peaks in the spectral density, approach values on the order of the inverse Fermi energy. These results are consistent with the "breakdown of Fermi-liquid theory" observed in recent experiments. © 2015 American Physical Society.