We have a 900W coffee maker that takes 10 minutes to brew a pot of coffee using a 1200W inverter. It uses 11 amps over that 10 minutes. We typically make coffee in the morning, when the batteries are about 70 percent full. The battery voltage drops from 12.5 down to about 12 during the brewing and typically returns to 12.5 when it is done. We have 4 6V 220AH AGM batteries.
So, my guess would be it will take at least 25amps and will be possible with at least 4 batteries that are 3/4 charged.
Would I do it with my set up? Yes. But we try not to make pots of coffee when the batteries are less than 65 percent full. The current draw would take the batteries below 11.9V - the cut off point at which I set my inverter.
Hope that helps.