My DF and I live in a 2 bedroom apartment and right now he is the only one working. It's hard, but we've been able to make it on just his income. I recommend doing cloth diapers and breastfeeding if you can. Babies themselves generally aren't as expensive as everyone thinks as they don't need much (most of the stuff we get for them is simply nice to have). It's when your baby gets older and becomes a child that the cost of raising them really goes up.
You can always co-sleep to save money on a crib, cloth diaper so that you can reuse them instead of buying disposables all the time, and breastfeed because it's free from day one.
I breastfeed and it's probably cut down our baby costs substantially since we don't have to buy formula as it gets very expensive.
Cloth diapers cost quite a bit upfront, but there are inexpensive ones out there on sites like lovelypocketdiapers.com and kerrbearkids.com and it saves you money in the long run as it doesn't up your laundry costs by much and disposables add up after a while where as cloth diapers are a one time cost and you can reuse them for all of your babies.
It really all depends on your living situation and how much your SO makes a year. My DF only makes about $25,000 a year at most, but we make it work by living in a reasonably priced apartment instead of buying a house and we're very careful with our money (we spend the bare minimum on groceries and we don't have a whole lot of "fun money" to work with). It's really rough living on one income though, sometimes it's just not possible. We've been fortunate to be able to do it, but there's a difference between surviving and being comfortable. We'll be sitting pretty when I'm working again.