How much Breast milk freezer space?

I'm a FTM. For those mommies who have experience breastfeeding and pumping, how much milk is typical to need to store? I'll be breastfeeding exclusively as long as possible, but when I go back to work after 6 weeks, I'll need to pump too. My husband doesn't think we need a deep freezer, but we barely have space in our freezer as it is. Just wondering how it worked for you!