If the only AC component you want to power is the TV, a point of use inverter (rather than a whole camper) will do the trick.
Look on the specifications tab (internet) or the back of the TV or TV/DVD you want to buy for the wattage required and buy a 12VDC to 120VAC inverter at least 10% higher than that.
The basics of TV power - CNET Reviews
Suggests that a 400 watt inverter will do what you need to do, just make sure your 12 volt wiring to the inverter is correctly sized and fused for 40 amps DC.
DC Wire Table
#8 or larger (smaller numbers as it gets bigger in diameter) will handle 8 feet from battery to inverter. See chart for longer runs.
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW