A.C.
I am very familiar with this topic, as our third child just turned five weeks old. Before we left the hospital, we were told that it is very normal for newborns to want to sleep all the time....meaning through feedings and everything. I think we all expect newborns to sleep a lot, but we also expect them to want to feed! This isn't always the case at first. We were told to never allow baby to go longer than 3 hours between nursing during the day and never longer than 4 hours at night. Yes it sucks, but this means that you may need to set a timer and work hard to wake baby up for feedings. As baby gets bigger, and is showing appropriate signs of growth (weight gain, wet diapers, etc.), then you can go longer between feedings (although I would suggest forcing yourself to stick to the 3 hours tops between feedings during the day so that you get your longer stretches at night -- at least until baby is 7 or 8 months old). For right now, wake baby up for feedings and set the timer so you don't go too long. Change baby's diaper before feedings to help wake him up. Leave him undressed if you need to. Use a cool washcloth on his feet if you're desperate. Strategically schedule bath time before a feeding. Make sure the room is nice and bright. Also remember that it is natural for baby to take about 3 gulps, then pause for a breath, then take three more gulps, etc.
Know that this is probably quite normal, but do keep an eye on things. It shouldn't last for long....all of our babies were much more alert after about 2 weeks. Our babies were also growing well and able to sleep through the night at 6 and 7 weeks respectively (we'll see on baby #3) -- exclusively breastfed as well.
Good luck and congratulations!