Preliminary results from a Fermilab study of the sensitivity for Higgs production at the Tevatron in the coming data taking are presented. The study extends existing results by systematically combining results for all decay channels, considering the production of higher mass Higgs bosons and interpreting the results in the context of supersymmetric Higgs production as well as standard model production. In addition new analysis methods are used. These significantly improve sensitivity. ©2000 American Institute of Physics.