“The Bible’s purpose is not so much to show you how to live a good life. The Bible’s purpose is to show you how God’s grace breaks into your life against your will and saves you from the sin and brokenness otherwise you would never be able to overcome…”
-Tim Keller
GRACE & PEACE 
I have to disagree with Mr. Keller in the sense of it being against your will… The Bible says, whosoever will let him come and drink of the waters of life freely.
Now it is true that without the grace of God we have no hope of being able to accomplish this.
I think I understand your concern. I suspect that what Keller is talking about it that, prior to regeneration, our will is at enmity with God. By his grace he opens our blind eyes – we did not ask him to do it – and then, once we see, we desire his grace.
Wow… thanks for clarifying that… you illustrated that well.