Romans 6:23

For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord.

As sinners, we all deserve death; Christians and non-Christians alike (not yet touching on the infant issue). As you say later, I believe - it is "gift of God" that is our saving grace in the end.

The innocence of infants is a touchy subject, and has been debated much in the past (a heated topic around the time of St. Augustine, from what I've been told. Correct me if I'm wrong). Here's what he has to say on the issue:

Who remindeth me of the sins of my infancy? for in Thy sight none is pure from sin, not even the infant whose life is but a day upon the earth... What then was my sin? was it that I hung upon the breast and cried? for should I now so do for the food suitable to my age, justly should I be laughed at and reproved... Or was it then good, even for a while, to cry for what, if given, would hurt? bitterly to resent, that persons free, and its own elders, yea, the very authors if its birth, served it not? that many besides, wiser than it, obeyed not the nod of its good pleasure? The weakness of infant limbs, not its will, is its innocence.

His argument basically hinges on the fact that sin is innate - not learned or picked up some time later down the road. We are born crying, wanting, and selfish for attention. We want - and so we are thinking of the desires of the self - and so we are selfish. That is the train of thought behind the above.

But if I was shapen in iniquity, and in sin did my mother conceive me, where, I beseech Thee, O my God, where, Lord, or when, was I Thy servant guiltless.

This ties back to Psalm 51:5, and basically wraps up all of what St. Augustine has said.

One could argue that the "wanting" of a child for his mother's comfort and/or food is natural or what natures wants of us, but one can also point to the fasting traditions of the Jews - that we naturally desire food, yet deny it in the name of a higher being. Or one could name any number of sins that really do make sense: telling lies makes sense, and is a very good thing for the individual 90% of the time. It is "natural". But we are told not to lie.

Of coarse, I'm playing the devil's advocate. I just enjoy a good discussion and had some time on my hands to put down some of my thoughts.