Lspangler,
Note 2oldman and smkettner's responses. You haven't taken into account the conversion inefficiency of the inverter (1450 watts AC out will require more than 1450 watts DC in) as well as Peukarts. I won't claim to know the details of Peukarts law, but it essentially describes the non-linear relationship between storage capacity and discharge capacity. You will be pulling 175+ amps, not the 25 amps that the Ah ratings are based on. And like they said, it is the voltage drop that will cut the inverter out. This means as the Keurig is pulling gobs of amperage, the battery voltage will sag down. The battery voltage will quickly drop to below the inverter's low voltage setpoint, probably around 11 volts. Once that happens, the inverter shuts down. With 2 GC batteries, I'd guess that happens within seconds to less than a minute. The battery voltage will recover some after the load is removed, but as mentioned you will require extra recharge time to fully replace what was removed.
I have tried to run my microwave off of my 1500 watt PSW inverter and 2 GC batteries and it only lasts a few seconds before the inverter shuts down. My inverter has adequate wiring.