Light Heavy MSSM Higgs Bosons at Large tan $\beta$

The region of MSSM Higgs parameter space currently excluded by the CDF Collaboration, based on an analysis of ~1 fb^-1 of integrated luminosity, is less than the expected sensitivity. We analyze the potential implications of the persistence of this discrepancy within the MSSM, assuming that the soft supersymmetry-breaking contributions to scalar masses are universal, apart from those to the Higgs masses (the NUHM model). We find that a light heavy MSSM Higgs signal in the unexcluded part of the sensitive region could indeed be accommodated in this simple model, even after taking into account other constraints from cold dark matter, electroweak precision observables and B physics observables. In this case the NUHM suggests that supersymmetric signatures should also be detectable in the near future in some other measurements such as BR(B_s -> mu+ mu-), BR(b -> s gamma) and (g-2)_mu, and M_h would have to be very close to the LEP exclusion limit. In addition, the dark matter candidate associated with this model should be on the verge of detection in direct detection experiments.