  Starting from {\it ab-initio} band structure for Na$_x$CoO$_2$, we derive the
single-electron energies and the effective tight-binding description for the
$t_{2g}$ bands using a projection procedure. We find that due to the presence
of the next-nearest-neighbor hoppings a local minimum in the electronic
dispersion close to the $\Gamma$ point of the first Brillouin zone forms.
Therefore, in addition to a large Fermi surface an electron pocket close to the
$\Gamma$ point emerges at high doping concentrations. The latter yields the new
scattering channel resulting in a peak structure of the itinerant magnetic
susceptibility at small momenta. This indicates itinerant in-plane
ferromagnetic state above certain critical concentration $x_m$, in agreement
with neutron scattering data. Below $x_m$ the magnetic susceptibility shows a
tendency towards the antiferromagnetic fluctuations. We estimate the value of
$0.58 < x_m < 0.7$ within the rigid band model and within the Hubbard model
with infinite on-site Coulomb repulsion consistent with the experimental phase
diagram.
