The generator, at full load, should use 1.5g or less of fuel per hour. If you take an eight hour overnight break, I'd expect no more than 10 gallons of fuel, costing less than $20 (US) now. That's less than an RV park and will let you run an electric heater or two. Of course, tihs doesn't include maintenance costs for the generator.
Our 33' 2011 Georgetown with its two 12V house batteries can't make it overnight when it's cold, the furnace is running, and we're boondocking. It usually takes around six hours to drain the batteries to the point where the propane/CO alarm activates as the furnace kicks on because it detects low battery voltage. My solution, a third house battery, will let us go overnight without problems.
When the house batteries need replacing, I'm switching to two 6V golf cart batteries and will be installing a multi-stage converter. The current third house battery will be kept and used only for its intended purpose, something not related to the RV.