  We report a systematic study of high magnetic field specific heat and
resistivity in single crystals of CeCoIn_5 for the field oriented in the basal
plane (H//ab) of this tetragonal heavy fermion superconductor. We observe a
divergent electronic specific heat as well as an enhanced A coefficient of the
T^{2} law in resistivity at the lowest temperatures, as the field approaches
the upper critical field of the superconducting transition. Together with the
results for field along the tetragonal axis (H//c), the emergent picture is
that of a magnetic field tuned quantum critical point which exists in the
vicinity of the superconducting H_{c2} despite a variation of a factor of 2.4
in H_{c2} for different field orientations. This suggests an underlying
physical reason exists for the superconducting H_{c2} to coincide with the
quantum critical field. Moreover, we show that the recovery of a Fermi Liquid
ground state with increasing magnetic field is more gradual, meaning that the
fluctuations responsible for the observed quantum critical phenomena are more
robust with respect to magnetic field, when the magnetic field is applied
in-plane. Together with the close proximity of the quantum critical point and
H_{c2} in CeCoIn_5 for both field orientation, the anisotropy in the recovery
of the Fermi liquid state might constitute an important piece of information in
identifying the nature of the fluctuations that become critical.
