Yes, if we we're in fact talking of making 1200 watts of 12v then 100 amps it would be but we're talking 12v and by a little magic with some silicon chips, miniature transformers and oscillators thrown into the mixer we are making 1200 watts of 110v power or 10.90 amps. Where I loose some of the math doing it in my head is the amount of 12v power needed for the inverter to step the power up to 110v and induce an alternating current to it. If the inverter we're 100% efficient (which they aren't as evidenced by the heat coming from one) then 10.90 amps of 12v would be enough. However unless your going to drop several $1,000 on a high end inverter (true sine wave with high efficiency) the stuff available and affordable to the trucking industry (modified sine wave) is closer to 60% to 70% efficient. Then you have the surge to charge everything inside the inverter so a safe bet for a 1200w inverter is a circuit capable of 30 amps minimum (20amps + 50% safety margin). A cigarette lighter plug (now known as a power port) is generally a 10 amp service but if you pull a constant 10 amps through the stock wiring it's going to get hot. The likely point of failure is the plug itself because your asking it to draw more power than is available so in turn it gets hot, sometimes very hot and fails. Plug you Coleman cooler into a standard power port then after a couple hours pull the plug and put your finger on the tip, at best it will be warm, at worst you'll have an educational burn on your finger. The two major points of failure on 12v electric heating things is either the plug or the thermostat. Both will fail due to inadequate supply amperage. All the above figures are based on 12v but when the engine is running the actual voltage should be somewhere between 13.5 and 14 so the same 30 amps needed at 12v becomes only 25 amps at 14v. So if you have a 900w inverter rated at 12v then in theory it should produce close to 1050 watts at 14v. Not even going to go into Ohms Law. My advice is don't plug a coffee maker into an inverter plugged into a power port. YMMV but the smell of burnt electrical wiring is hard to cover up when you take the truck to the shop. FWIW, I just measured a Mr. Coffee and it was showing 7.3 amps on commercial 110v (so closer to 120v) which is 876 watts. My Keurig was 9.1 amps 1092 watts and my DeLonghi espresso machine was 12.2 amps 1464 watts. I did not check the voltage here today but last time I checked with my Fluke the RMS was 119v so I'm using 120v for calculations just to be safe. Now with all of that, my DeLonghi will not work on a modified sine wave inverter (affordable), tried many times. Neither will my laser printer or a host of other things. Now on the other side of the coin, I have a power supply here that I use to make clean 12v power from 110v for my computerized LiPo chargers. I have pulled 142 amps of 12.7v (1803 watts) from it which was drawing almost 23 amps of 110v power (2530 watts).
I have a kurig but a few years ago I bought a pump type coffee holder it holds all the hazelnut coffee FYing J and Pilot make at one time, and I just pay the regular refill price and get the 10th pot free. $2.00 per pot of coffee, dont have to carry a coffee maker set a timer, or even have my inverter on. You can buy them at wallyworld for around $20.00.
The correct thing to do is what I did. In 1974 on my very first trip to West Africa, I met a man who gave me some Syrian Coffee. It was thick, like molasses. I can still taste it. The smell of coffee still brings back those horrible memories. Nasty stuff.
