Let's take a look at the math...
1.5 amps at 120V is 165 watts, but you need to be concerned about the draw on the battery. 165W at 13.8 volts is 12 amps. So, take a look at the amp-hour rating on your battery and that will give you an idea of how long it will last. A Group 27 deep cycle battery is typically 110AH capacity, but since the voltage drops as the battery is deleted the useable capacity is probably 80%, or 88AH, so at 12A draw you can probably go about 7 1/2 hours.
If you need longer, look at a small generator, or, if you have AC power available look at an invert-charger combo that has an auto transfer switch built in. The transfer switch will pass on the AC source when it in present, and the charger will maintain the battery charge. Then, if the AC source goes away the transfer switch will automatically switch to the battery and the inverter will supply power to the CTO.
BTW, is that 165W continuous, or is it the max? If it is the max spec you average amy be lower and you could run longer.