  Here we report the observation of Fermi surface (FS) pockets via the
Shubnikov de Haas effect in Na$_x$CoO$_2$ for $x = 0.71$ and 0.84,
respectively. Our observations indicate that the FS expected for each compound
intersects their corresponding Brillouin zones, as defined by the previously
reported superlattice structures, leading to small reconstructed FS pockets,
but only if a precise number of holes per unit cell is \emph{localized}. For
$0.71 \leq x < 0.75$ the coexistence of itinerant carriers and localized $S
=1/2$ spins on a paramagnetic triangular superlattice leads at low temperatures
to the observation of a deviation from standard Fermi-liquid behavior in the
electrical transport and heat capacity properties, suggesting the formation of
some kind of quantum spin-liquid ground state.
