How to calculate battery life with a given load?
Look at the power required = 120V * 6A = 720W using P=V*I.

Your battery which is DC has to run through an inverter to get to 120V AC.  There will probably be about 10% loss in efficiency, so add 10%

Lets call that power = 720+72 ~ 800W

How much current would the battery need to put out to generate 800W?

800W/18V ~ 44A.  (yes that is amps from I=P/V)

Your battery rated at 1.5 A-Hr would last about 1.5/44 = 0.034Hr or about 2 minutes.

This of course would never work.  As the internal resistance of your little battery would never allow such a massive discharge, and your whole system would most likely fail to even start turning the motor.