Well good for you for actually using the KillAWatt instead of guessing. It must be a flat screen tv as 45 watts would be low for a conventional tv unless it is really small. Anyway, if your load is roughly 60 watts total, that would be .5 amp at 120 VAC, or 5 amps at 12 volts which is what your power source is (Ohm's Law, V x A=W). However the inverter has some losses, especially a cheap one. Say 20% or so and you have a total load from your 12V
house battery of about 6 amps.
You then need to find the total rating of your house battery, but if you have 2 house batteries, each with a 60 amp/hour rating at 12 volts, you have 120 amp/hrs of capacity. That is roughly 120 amps for one hour, or 1 amp for 120 hrs, or anything in between. You don't want to drain them below 50% or it negatively impacts the life of the battery. So you have a useable 60 amp/hrs capacity, which is 10 hrs, with a 6 amp load. Assuming no other loads.
Hope that helps.