Not gonna vote because none of the answers really fits what I would say.
While I agree with you that it is possible, through the grace of God, to go a day without sinning, I would guess that no one has ever done it. Considering how difficult it is to keep our thoughts in check, and given God's command to do all to His glory, I would think that even the most righteous man who ever lived would slip at least once a day by doing or thinking something that is not to God's glory.
So, I guess my vote is for "possible, but insanely improbable."