  The Atlas and CMS collaborations have both reported an excess of events in
the WW\star \rightarrow \ell+\ell- + ETmiss search channel, which could be the
first evidence for the Higgs boson. In the context of the MSSM, the lightest
SUSY Higgs scalar h is expected to occur with mass mh = 135 GeV, depending on
the range of SUSY parameters scanned over. Since the h \rightarrow WW\star
branching fraction falls swiftly with decreasing mh, a signal in the WW\star
channel would favor an h at the high end of its predicted mass range. We scan
over general GUT scale SUSY model parameters to find those which give rise to
mh > 130 GeV. A value of m0 \sim 10 - 20 TeV is favored, with A0 \sim \pm2m0,
while the lower range of m1/2 < 1 TeV is also slightly favored. This gives rise
to an "effective SUSY" type of sparticle mass spectrum. For low m1/2, gluino
pair production followed by three-body gluino decay to top quarks may
ultimately be accesible to LHC searches, while for higher m1/2 values, the SUSY
spectra would likely be out of range of any conceivable LHC reach. Since the
thermal neutralino relic abundance tends to be very high, late-time entropy
dilution or neutralino decay to light axinos would be required to gain accord
with the measured dark matter abundance
