Mods have minimum resistances they will fire. It has nothing to do with battery current, it has to do with what the chip is designed to handle. They also have a voltage range they will output. When the resistance gets too low, some mods can't buck the output voltage low enough to give the set wattage so it won't fire. Nothing to do with battery current.
Multiply the nominal voltage (3.7v) of the batts we use by 20 amps and you get 74 watts. Each 20 amp batt is good for about that amount of watts and that's why single batt mods cap around there. Double for two cells, etc. Running 70 watts per batt with cells less than 20 amps results in exceeding the cells amp limit. Again, coil resistance has nothing to do with it.
Coil voltage and coil current are not the same as battery voltage and battery current. 4v and 20 amps at the coil doesn't mean the 2 cells in series that make 8v are also discharging 20 amps. 4 x 20 doesn't equal 8 x 20. Only the total watts being output equal the total watts being drawn from the batteries.
Bottom line, use quality 20 amp or higher batteries, run any resistance the mod will fire and use whatever watt setting you want to dial in and you're fine.