You missed something important in the text there, Al. It doesn't say, "We also know that the law is made not for the lawkeepers but for lawbreakers", it says, "We also know that the law is made not for the righteous but for lawbreakers."
Righteousness comes only through Christ. Christ did not come to make lawbreakers into lawkeepers; He came to make spiritually dead people into spiritually alive people. How? By giving them the Gift of Righteousness so that He could indwell them with His Holy Spirit (God cannot indwell a defiled Temple).
-JGIG