The nature of the normal state of an ultracold Fermi gas in the BCS-BEC crossover is an intriguing and controversial topic. While the many-body ground state is always a superfluid condensate of paired fermions, the normal state must evolve from a Fermi liquid to a Bose gas of molecules as a function of the interaction strength. How this occurs is still largely unknown. We explore this question with measurements of the distribution of single-particle energies and momenta in a homogeneous gas above T_C. Fits to data taken for different interaction strengths reveal the onset of pairing and decreasing spectral weight (or quasiparticle residue, Z) for the Fermi liquid. We also extract the effective mass m, pair correlation length, and Tan’s contact. We find that Z vanishes abruptly, which signals the breakdown of a Fermi liquid description. Such a sharp change is surprising in the BCS-BEC crossover.