  The ground state of the Hubbard model with nearest-neighbor hopping on the
square lattice at half filling is known to be that of an antiferromagnetic
(AFM) band insulator for any on-site repulsion. At finite temperature, the
absence of long-range order makes the question of how the interaction-driven
insulator is realized nontrivial. We address this problem with controlled
accuracy in the thermodynamic limit using self-energy diagrammatic determinant
Monte Carlo and dynamical cluster approximation methods and show that
development of long-range AFM correlations drives an extended crossover from
Fermi liquid to insulating behavior in the parameter regime that precludes a
metal-to-insulator transition. The intermediate crossover state is best
described as a non-Fermi liquid with a partially gapped Fermi surface.
