  We examine the capability of a $\sqrt{s}=2$ TeV Tevatron $p\bar p$ collider
to discover supersymmetry, given a luminosity upgrade to amass $25\ fb^{-1}$ of
data. We compare with the corresponding reach of the Tevatron Main Injector
($1\ fb^{-1}$ of data). Working within the framework of minimal supergravity
with gauge coupling unification and radiative electroweak symmetry breaking, we
first calculate the regions of parameter space accessible via the clean
trilepton signal from $\tw_1\tz_2\to 3\ell +\eslt$ production, with detailed
event generation of both signal and major physics backgrounds. The trilepton
signal can allow equivalent gluino masses of up to $m_{\tg}\sim 600-700$ GeV to
be probed if $m_0$ is small. If $m_0$ is large, then $m_{\tg}\sim 500$ GeV can
be probed for $\mu <0$; however, for $\mu >0$ and large values of $m_0$, the
rate for $\tz_2\to\tz_1\ell\bar{\ell}$ is suppressed by interference effects,
and there is {\it no} reach in this channel. We also examine regions where the
signal from $\tw_1\overline{\tw_1}\to \ell\bar{\ell}+\eslt$ is detectable.
Although this signal is background limited, it is observable in some regions
where the clean trilepton signal is too small. Finally, the signal
$\tw_1\tz_2\to jets+\ell\bar{\ell} +\eslt$ can confirm the clean trilepton
signal in a substantial subset of the parameter space where the trilepton
signal can be seen. We note that although the clean trilepton signal may allow
Tevatron experiments to identify signals in regions of parameter space beyond
the reach of LEP II, the dilepton channels generally probe much the same region
as LEP II.
