My understanding is the SlingBox does not have a tuner so basically you can only "Sling" (digitize) the output of your detuned video (cable box or TV), to your home network. You then watch video with your favorite app (Desktop or mobile).
I was in the same boat as you and I decided that an antenna was the best solution.
An antenna will give you backup in case your cable fails AND you may give you clearer video. Cable companies compress signals before they transmit so off air video can look better. It depends where your live.
This device may interest you. It has THREE tuners so it can support multiple users. You rent a CableCard from your cable provider for only a couple of bucks.
SiliconDust HDHomeRun PRIME 3-Tuner DLNA/UPnP Compatible Streaming Media Player, HDHR3-CC