Will not work. The Zenith is not compatible with cable HDTV, unless your local cableco passes OTA type (8VSB) signals. Most all cableco's use QAM for HDTV, and there are no OTA, Dish, DirecTV STB's that will decode QAM.
If you have a Mitsu HDTV that is compatible with the Promise Module, or one of the newer integrated Mitsu HDTV, you would be able to receive the QAM unscrambled HDTV cable channels, which would probably be local HDTV. Usually cableco's scramble the QAM premium channels like HBO, Showtime, etc., and the Mitus will not decoded them.
In most all cases, the cableco will rent you a STB just for their HDTV & digital cable service.