My milk didn't come in for at least a week. My LO wasn't getting enough nutrients and became lethargic. I tried and tried to breast feed, saw a lactation specialist, and when I realized that he wasn't getting enough nutrients we supplemented with formula. For weeks I kept trying to pump at least 7-9 times a day and never got more than 3 oz combined at a time. Only a few times did my breast milk actually leak out.
So, I decided that instead of stressing and dedicating so much time to something that obviously wasn't working out, that we would use formula. Personally, it upsets talk about it. I feel like I let my child down but I know that I did try and that is what matters. There is always the next one!
This is similar to my experience, except I never got a milk supply at all. We had to give DD formula from day 4 when we realized she was so dehydrated she had crystals in her urine. I saw an LC immediately, rented a hospital grade pump, and starting taking herbal supplements to improve my supply. The first time I pumped for 20 minutes, and got one-eighth of a teaspoon out of both breasts combined. After a month of using the pump for hours every day, I still maxed out at only about one ounce total for the entire day. Most pumping sessions I got as little as 3-5 ml. I stopped after a month because I felt like I was spending so much time attached to the pump and stressing over it that I was actually not able to bond with my baby the way I wanted to.
I have a condition called IGT (insufficient glandular tissue). They are not 100% sure what causes low milk supply, but there are some links with hormonal imbalances, some are physical causes like mine. Many LCs have told me that it seems to be increasingly common -- one theory is that it was caused by endocrine disrupters our mothers where exposed to while we were in utero. There is also possibly a genetic component.
To the PP, depending on the cause, there are some things you might be able to do ahead of time to increase your chance of having greater success next time. I would recommend talking to a knowledgable LC for an assessment ahead of time, if you want to try again in the future. And please don't blame yourself. I know exactly how bad it feels to want to breastfeed your child and feel like a failure. I struggled with that for a long time, but have finally come to terms with it.
Here are a couple of links with good info: