According to this guy a modern LCD TV uses about 1A. Conservatively, for a 12V TV, that would be about 12W.
Assuming 2X 6V batteries, you will have 265Amps to play with. BUT you will only want to drain them to 50%. So, not including losses, you can use down to 116A or so.
IN THEORY, if you didn't use your batteries for anything else, you could estimate that you could watch TV all day and then some. Maybe 12 hours or so.
Someone check my math.