  Motivated by the recent discovery of superconductivity in Ca- and
Yb-intercalated graphite (CaC$_{6}$ and YbC$_{6}$) and from the ongoing debate
on the nature and role of the interlayer state in this class of compounds, in
this work we critically study the electron-phonon properties of a simple model
based on primitive graphite. We show that this model captures an essential
feature of the electron-phonon properties of the Graphite Intercalation
Compounds (GICs), namely, the existence of a strong dormant electron-phonon
interaction between interlayer and $\pi ^{\ast}$ electrons, for which we
provide a simple geometrical explanation in terms of NMTO Wannier-like
functions. Our findings correct the oversimplified view that
nearly-free-electron states cannot interact with the surrounding lattice, and
explain the empirical correlation between the filling of the interlayer band
and the occurrence of superconductivity in Graphite-Intercalation Compounds.
