How many batteries and how big are they? What is the rating on the TV so you can tell how much power it will use? You need enough battery power to power your inverter, plus the other things that will drain the batteries, over night.
Example:
TV + reciever uses 200 watts
(2) 90 amp-hour 12-volt batteries
5 hours of TV usage is 4 x 200 / 12 volts or 67 amp-hours from your batteries if the inverter were 100% efficient, realistically it would be 85% efficient so 67 / 0.85 = 79 amp-hours just from the TV.
Now you should not run batteries down to less than 50% so you only have 90 amp-hours to work with in this example. A couple little lights, your carbon-dioxide detector, your LP detector, the fridge, etc. will use more the the 11 amp-hours left. In this case you better run the generator at least some of the time. If you had four batteries you would be fine in this example.

You could also put in an inverter and run the generator for the first two hours and save on fuel.

That just talks if it is possible.

Now about cost:
Most generators run between 0.3 and 0.75 gallons of fuel per hour. 4 hours at worst case is 3 gallons of fuel. Ten nights per year would be 30 gallons or about $90 give or take. If you pay someone to put in an inverter expect it to be $300 to $500 so you would need to use it 33 or more evenings to break even at the cheapest install cost. If you do it yourself you could probably get away with $40 to $75 for the inverter and wire and it would pay for itself in under 10 nights.

-- Edited by bjoyce at 15:32, 2007-10-13