Is it possible to run out of milk?

I have a 10 day old baby and I pump once a day so I have two bottles ready for night time feedings for dad. I would like to pump more so dad can be more involved in the feedings also, but I'm afraid that I won't have enough milk. What if she wakes up right after I'm done pumping? Will there still be enough milk in there to feed her? I just feel like if my aren't engorged or if they "feel" like there's no milk in there, then there isn't? Can you run out of milk? And how often can I pump?