Check the specifications for the Peltier. Power consumption of those gadgets is complex. If you tweak the voltage, then the current consumption will go down. Also, those specs assume a specified hot and cold side temperature for the Peltier, and those values will also affect the electrical behavior of the peltier. Very touchy feedback loops are all over the place with peltiers that way.
A general trend I have seen with pelts is to expect about twice the power consumption in watts as the heat removal function. At 12 volts, I would guess probably a eight amp draw or so from that thing, or ~100-110W off the power supply....should be doable with the one you have. At twelve volts, the heat work function would probably drop somewhat lower as well, perhaps ~60W?
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