You should be able to make it through one maybe two nights on your battery. Make sure you keep your frig on gas and not auto. That also seems to drain the battery a little faster. I bought a champion 3500 watt generator for $279 at Cabelas last year. Works good and not too noisy. I take it along when boondocking and saves me the worry about draining my battery.
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2011 Lacrosse 318BHS Touring Edition
2012 Ford F150 SupCrew 4x4 XLT 6.5' Max Tow