  We report the formation and observation of an electron liquid in
Sr$_{2-x}$La$_{x}$TiO$_4$, the quasi-two-dimensional counterpart of SrTiO$_3$,
through reactive molecular-beam epitaxy and {\it in situ} angle-resolved
photoemission spectroscopy. The lowest lying states are found to be comprised
of Ti 3$d_{xy}$ orbitals, analogous to the LaAlO$_3$/SrTiO$_3$ interface and
exhibit unusually broad features characterized by quantized energy levels and a
reduced Luttinger volume. Using model calculations, we explain these
characteristics through an interplay of disorder and electron-phonon coupling
acting co-operatively at similar energy scales, which provides a possible
mechanism for explaining the low free carrier concentrations observed at
various oxide heterostructures such as the LaAlO$_3$/SrTiO$_3$ interface.
