  Charge frustration due to further neighbor Coulomb repulsion can have
dramatic effects on the electronic properties of Na$_x$CoO$_2$ in the full
doping range. It can significantly reduce the effective mobility of the charge
carriers, leading to a low degeneracy temperature $\epsilon_F \lesssim T$. Such
strongly renormalized Fermi liquid has rather unusual properties--from the
point of view of the ordinary metals with $\epsilon_F \gg T$--but similar to
the properties that are actually observed in the Na$_x$CoO$_2$ system. For
example, we show that the anomalous thermopower and Hall effect observed in
Na$_{0.7}$CoO$_2$ may be interpreted along these lines. If the repulsion is
strong, it can also lead to charge order; nevertheless, away from the
commensurate dopings, the configurational constraints allow some mobility for
the charge carriers, i.e., there remains some ``metallic'' component. Finally,
the particularly strong bandwidth suppression around the commensurate $x=1/3$
can help resurrect the RVB superconductivity, which would otherwise not be
expected near this high doping. These suggestions are demonstrated specifically
for a $tJ$-like model with an additional nearest neighbor repulsion.
