In the context of the MSSM the Light Stop Scenario (LSS) is the only region of parameter space that allows for successful Electroweak Baryogenesis (EWBG). This possibility is very phenomenologically attractive, since it allows for the direct production of light stops and could be tested at the LHC. The ATLAS and CMS experiments have recently supplied tantalizing hints for a Higgs boson with a mass of ~ 125 GeV. This Higgs mass severely restricts the parameter space of the LSS, and we discuss the specific predictions made for EWBG in the MSSM. Combining data from all the available ATLAS and CMS Higgs searches reveals a tension with the predictions of EWBG even at this early stage. This allows us to exclude EWBG in the MSSM at greater than (90) 95% confidence level in the (non-)decoupling limit, by examining correlations between different Higgs decay channels. We also examine the exclusion without the assumption of a ~ 125 GeV Higgs. The Higgs searches are still highly constraining, excluding the entire EWBG parameter space at greater than 90% CL except for a small window of m_h ~ 117 - 119 GeV.