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According to this page, 298 Senators have died in office (it does not include the last member to die, who died in 2010. I included him in the previously stated number).
According to this page, 815 House Representatives have died in office (it does not include the last three members to die in office. I included them in the previously stated number).
Our grand total is 1113 US congressmen to die in office since the 1st US Congress in 1789, as of April 25, 2012.
Other sources- Members of Congress Who Die in Office: Historic and Current Practices