@buton:
As stated by @pylon above, given that you are using an SPI-based pressure sensor, the only way using the pressure sensor itself to make the inference about that threshold would be to take measurements once every X milliseconds/seconds, and go to sleep, unless threshold crossed. This is a reliable way to do it -- and draws hardly any power (actually negligible compared to the self-discharge of a Li-ion); remember that a microcontroller like on an Arduino processes the measurement (a few instruction cycles) in much less than a millisecond, and then goes to sleep, where the current draw is very close to zero.
Also, a sidenote: just took a look at your webpage parts list for this project. You could REALLY cut down on the parts cost (and earn a little extra margin on your Kickstarter) if you make your own board instead of trying to assimilate all those individual modules (but you probably know this and have different reasons?)