Often at TV locations in motorhomes there will be a 12V lighter socket installed. A small inverter with a lighter cord will easily power a modern LCD TV (and DVD player and so forth), and installation consists of plugging stuff in and putting it on a shelf or whatever.
You shouldn't need to worry at all about running the house batteries down from this while underway because there is a system to charge them from the vehicle alternator that should be very easily able to keep up with this sort of usage. If this system isn't working properly, I'd suggest fixing it; one common fault is the relay that connects the batteries together.
