1.8 ohm nichrome is .18mm/33gauge/.007in wire. That's the size used in "e-cigarettes", and given the size of those devices it's not unlikely that 20ma might be a good place to start. Too much current and you'll burn the wire.
I'd suggest trying the nichrome coil with a 220 ohm resistor in series and connect that to the battery. See if it gets the coil hot enough but not so hot that it burns out.
Ideally you'd use a thermistor in contact with the nichrome coil (maybe even wrapped around the thermistor) for temperature feedback. Then you could feed the coil current until you reach the required temperature and then use PWM to back off on the current. The problem you have is that as soon as someone inhales the coil will cool off and you want to be able to ramp the temperature back up to compensate.