  Normal states of the attractive Hubbard model, especially in two dimension,
are studied in the light of a transition from a Fermi liquid to an insulating
or gapped state. A series of variational Monte Carlo calculations with better
statistics is carried out to estimate accurately expectation values by several
many-body wave functions. Although a relatively clear crossover is observed
even in the plain Gutzwiller wave function, the states in both regimes are
metallic. Meanwhile, a substantial metal-insulator transition takes place at
|U|\sim W (band width) in an improved wave function in which intersite
correlation is introduced by taking account of virtual states in the
second-order perturbation in the infinite-|U| limit. The critical value is
favorably compared with recent results of the dynamical-mean-field
approximation. In contrast, a conventional Jastrow-type wave functions scarcely
improve the normal state. In addition, the issue of Brinkman-Rice
metal-insulator transition is reconsidered with much larger systems.
