When I was a first time mother, I was exhausted. All the time. I remember distinctly screaming at my newborn child one day because he refused to nap and cried every time I put him down and I was exhausted. I expected much worse the second time around. But so far (knock wood) it has been okay.
I think the reason for this is because I have become what I like to think of as a sleep scavenger. I will take sleep in any form whenever I can get it. This includes turning on a DVD for the tot and snoozing in front of the tv with him while the baby sleeps in her rocker. I have become artful at trying to encourage the baby to nurse and nap during the toddlers nap - scoring myself a minimum of an overlapping forty-five minutes of peace. This probably doesn't seem like much when you are only getting 4-5 hours of sleep at night, but couple that with grabbing an hour in the evening when the husband gets home or first thing in the morning when he's getting up and drinking his coffee and it can come close to a full night of sleep. Which makes it so much easier to relax and almost enjoy those 3am feedings.