We investigate the model independent nature of the Supersymmetry search
strategies at the 7 TeV LHC. To this end, we study the
missing-transverse-energy-based searches developed by the ATLAS Collaboration
that were essentially designed for mSUGRA. We simulate the signals for ~71k
models in the 19-dimensional parameter space of the pMSSM. These models have
been found to satisfy existing experimental and theoretical constraints and
provide insight into general features of the MSSM without reference to a
particular SUSY breaking scenario or any other assumptions at the GUT scale.
Using backgrounds generated by ATLAS, we find that imprecise knowledge of these
estimated backgrounds is a limiting factor in the potential discovery of these
models and that some channels become systematics-limited at larger
luminosities. As this systematic error is varied between 20-100%, roughly half
to 90% of this model sample is observable with significance S>5 for 1 fb^{-1}
of integrated luminosity. We then examine the model characteristics for the
cases which cannot be discovered and find several contributing factors. We find
that a blanket statement that squarks and gluinos are excluded with masses
below a specific value cannot be made. We next explore possible modifications
to the kinematic cuts in these analyses that may improve the pMSSM model
coverage. Lastly, we examine the implications of a null search at the 7 TeV LHC
in terms of the degree of fine-tuning that would be present in this model set
and for sparticle production at the 500 GeV and 1 TeV Linear Collider.Comment: 51 pages, 26 figure