Before I kill my Teensy 3.1, I want to run my board from a CR2032 battery.
The CR2032 is rated at 3.0V, so it may very well work for a short time. A CR2032 is usually used just to keep the RTC circuits alive when other power sources have been switched off. So unless you severely limit power consumption (deep sleep followed by short bursts of activity) I doubt your teensy will be able to subsist for long on a tiny battery like that.
wouldn't 3.0V w/new battery, and less as the CR2032 discharges, give no or too-little margin?