I am trying to use a date variable with select by attributes against a shapefile and am having a similar problem. Modelbuilder's date type variable reformats the needed date format that I type in...yyyy-mm-dd to mm/dd/yyyy. Of course this mm/dd/yyyy format does not work with a shapefile. The documentation states that SQL used against a date column in a shapefile needs to be formatted as date 'yyyy-mm-dd'.
Working with ArcGIS Desktop 10.01, service pack 5.
Please bring back the old arcgis forums.