A Conception of God I Don't Understand

I was reading an article by John Piper titled "Did the Death of Jesus Accomplish Anything for the Non-Elect?" and was struck by these comments:

In one sense, as soon as we sin we should be punished eternally. We shouldn't get another breath. There should be no reprieve. There should be no time given to us. So clearly then, in some sense, the time given to us is grace. And grace for a sinner requires some kind of payment or purchase or warrant from a holy God. And Christ would be the one who provides that.

I can't imagine a God we lovingly call Abba punishing eternally as soon as we sin. I just don't get that. Maybe it's because the lens through which I view God is Christ. I don't know. But statements like that make me shiver and run from someone who rambles on in that fashion.

I don't think I could turn my will and my life over to a God that, as soon as I make a mistake, would eternally punish me.