I wish someone would take this baby away for a few days while I sleep. Does that make me a bad mother?
No, it makes you normal. Your exhaustion has no implications for your love for your child, or your maternal abilities. Hang in there -- it gets better. In the meantime, ask for help. Have someone (your partner? your mom? a friend?) take over baby duty for an afternoon while you sleep between feedings. Also ask someone to go to the grocery store for you, or to cook. Seriously -- take advantage of all the help you can get. You deserve it.
Plus, more from The Bump:
New Mom Survival Guide
Best and Worst Things About Having a Newborn
10 Things to Do For You In 10 Minutes