There is a passage in the New Testament that says, I paraphrase: Every morning I wake up a new person. Or: Every morning I am born a new man. I think Apostle Peter or Apostle Paul is speaking it. Can someone help me track the exact quote with textual reference? Thanks.
I believe you're thinking of 2 Corinthians 5:17 (KJV)
It's not "every morning" but it is the passage that comes to mind with the teaching that we are made new. It deals with out new relationship in Christ after salvation.
In the Old Testament, there is Lamentations 3:22-23 (KJV)
If neither of these are what you're thinking of, you can search many versions of the Bible at http://www.biblegateway.com/passage/?search=Lamentations+3%3A22-23&version=KJV
Here is where Paul says, "I die every day."