  Deviations from Fermi liquid behavior are well documented in the normal state
of the cuprate superconductors, and some of these differences seem to be
related to pre-transitional features appearing at temperatures above T$_c$. The
observation of a pseudogap, e.g. in ARPES experiments, is a familiar example of
this physics. One potential explanation for this behaviour involves preformed
pairs with finite lifetimes existing in the normal state above T$_c$. In this
way two characteristic temperatures can be established. A higher one T$^*$ at
which pairs begin to form and the actual T$_c$ at which a phase-coherent
superconducting phase is established.
  In order to test these ideas we have investigated the negative U Hubbard
model in two dimensions in the fully self-consistent ladder approximation at
low electron densities. In the non self-consistent version of this theory the
system always shows an instability towards Bose-condensation of infinite
lifetime pairs. In contrast to this, pairs obtain a finite lifetime due to
pair-pair interaction and the sharp two-particle bound state is strongly
lifetime broadened when self-consistency is applied. A quasi-particle
scattering rate which varies linearly with temperature is also found. The fully
self-consistent calculation we were able to perform using a ${\bf {\vec
k}}$--averaged approximation in which the self-energy loses its ${\bf {\vec
k}}$-dispersion due to a ${\bf {\vec k}}$-average. This approximation is found
to preserve the essential physics.
