How long can you last on 3-4 hours of sleep?

Not much longer for me it would seem. This state of not getting enough sleep is getting to me. I'm tired, my temper and emotions are shorting out at a faster rate, and I think my sanity is just about to give way.

She wants to feed every other hour. Each feed lasts between 30-40 mins. There's usually a need for a diaper change in between. That usually takes another 5-10 mins. Sometimes, KM helps me. Most times I try to let him sleep unless I feel I really could do with a little more help. Then I need to burp her or at least keep her upright for another 5-10 mins. Therefore, if like today, she wakes up at 3.10am for a feed & change, I'm not done with her till about now - 4am. And if she needs to feed hourly, she could be up in another 10-15 mins. If I'm lucky and she decides to feed in 2 hours, I might be able to get at least 30-45 mins of sleep in between, considering I'm not normally able to fall asleep upon contact with my pillow. This pattern will last through the day until the next night. It has been like that for almost a week. I blog, typing with one hand while she feeds. This logging helps me maintain some bit of sanity, pulling my thoughts together in an attempt to find some coherence in me still.

I am tired. I am quick-tempered because I am tired. I am upset that my fuse is running so short. But I am tired. I feel bad that I feel so tired. Yet how can I not feel tired? I want time for myself. I feel guilty when I do find time for myself. But I need time for myself, to myself. I don't want visitors. He cancelled all visits from his relatives and friends. I'm grateful, but he seems angry with me. I am upset that he's angry, but I am tired. So very tired. I wish I needn't have to feed her, so I can sleep. How can I be thinking something like that? I love her. But I am so tired. I'm in tears.