I had a situation occur the other day with my 2012 Volt. The battery in the remote died and I couldn't start my car! Yikes!
That's a big issue! The remote takes a common watch battery. I could key into the car just fine using the physical key but couldn't start the car without the car sensing the remote is inside (which didn't happen if the battery is dead). Once I replaced the battery in the remote I could start the car just fine.
Lesson learned: keep a spare battery for the remote in your car!!!!