Yup, your input doesn't have a snowball's chance of keeping up with your output.
At 2000W, your inverter will be drawing at least 167 Amps. 63 Amps in vs. 167 Amps out = 104 Amps shortage.
Also keep in mind that a 63 Amp alternator is not designed to output 63 Amps running a fridge or furnace during a sustained power outage. It's only meant to run like that for a few minutes to top off the car battery after a start.
...and before you say something about how many cold cranking Amps your battery has, forget it. CCA rating is only meant to be sustained for a few seconds while you start the car, not running a fridge or furnace during a sustained power outage.
Same goes for that inverter. Even though it says 2000W continuous it is likely not capable of sustaining 2000W indefinitely.
You've got a good idea there for cheap electrical power, just not on the scale you expect to be using it. Charging tractor batteries, running tools and lights in a remote shed.
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