  The search for MSSM Higgs bosons will be an important goal at the LHC. We
analyze the search reach of the CMS experiment for the heavy neutral MSSM Higgs
bosons with an integrated luminosity of 30 or 60 fb^-1. This is done by
combining the latest results for the CMS experimental sensitivities based on
full simulation studies with state-of-the-art theoretical predictions of MSSM
Higgs-boson properties. The results are interpreted in MSSM benchmark scenarios
in terms of the parameters tan_beta and the Higgs-boson mass scale, M_A. We
study the dependence of the 5 sigma discovery contours in the M_A-tan_beta
plane on variations of the other supersymmetric parameters. The largest effects
arise from a change in the higgsino mass parameter mu, which enters both via
higher-order radiative corrections and via the kinematics of Higgs decays into
supersymmetric particles. While the variation of $\mu$ can shift the
prospective discovery reach (and correspondingly the ``LHC wedge'' region) by
about Delta tan_beta = 10, we find that the discovery reach is rather stable
with respect to the impact of other supersymmetric parameters. Within the
discovery region we analyze the accuracy with which the masses of the heavy
neutral Higgs bosons can be determined. We find that an accuracy of 1-4% should
be achievable, which could make it possible in favourable regions of the MSSM
parameter space to experimentally resolve the signals of the two heavy MSSM
Higgs bosons at the LHC.
