Sleep deprivation is making me angry at my wife for no reason

We've got a newborn (8 days old) and a 2-year-old. I'm at the point where my wife breathes wrong and I want to snap at her. We're both running on like 3 hours of broken sleep. She snapped back at me yesterday and we had our first real fight since the baby came. I know it's the exhaustion talking but it's scary how thin my patience is. Anyone else experience this? Does it get better once you get actual sleep again?