  We examine the exclusion limits set by the CDF and D0 experiments on the
Standard Model Higgs boson mass from their searches at the Tevatron in the
light of large theoretical uncertainties on the signal and background cross
sections. We show that when these uncertainties are consistently taken into
account, the sensitivity of the experiments becomes significantly lower and the
currently excluded mass range $M_H=158$-175 GeV would be entirely reopened. The
necessary luminosity required to recover the current sensitivity is found to be
a factor of two higher than the present one.
