Bruce's Math above is impeccable, as always. I read only the Product Reviews; not the Forum opinions. I used a TEC w/a Deep Cycle Battery while building a House [Brand not recalled this second, but it wasn't a Coleman]. It worked fine for what they are. The cooling capacity depends on the size of the TEC Module and the outer wall Insulation. So long as you keep the TEC Vent clear, you could make an extra, outer Insulation 'box' of Poly Iso rigid Insulation, or something similar to improve performance.
If you go the Coleman TEC route, I'd propose a hybrid solution. I used to freeze things like Meat and put a few pieces in the Cooler, stored in double seal Zip Lok Bags. They'd thaw gradually while keeping the Cooler 'cooler' during the problematic Summer season, and I had only to do a lil Meal planning. Another standard tip is to put in only pre-cooled Pop and other items since the cooling capacity is not great enough to lower Food temps quickly and safely.
One of the Walmart Reviews mentioned making Ice in Bottles, and that's what I did. Or, to save space, you could make Ice in a Tupperware-style of sealed plastic 'Brownie' Box. This would lower internal Cooler temp as well while taking up the least space w/o water leakage. Ice lasts much longer in a TEC.
The Battery drawdown is what it is. You'd have to run a Genny, or a Solar Panel, to stretch Cooler operating time, depending on your Camping time.
I use several Radio Shack Indoor/Outdoor Temp Gauges for various applications. The outdoor Probe can go in the Cooler and provide hard data about Food temps, instead of guessing.
How TECs Work