I smell a legalist =D
(Ephesians 2:8-9) - "For by grace you have been saved through faith; and that not of yourselves, it is the gift of God; not as a result of works, that no one should boast."
(Rom. 3:20, 28) - "because by the works of the Law no flesh will be justified in His sight; for through the Law comes the knowledge of sin...For we maintain that a man is justified by faith apart from works of the Law."
(Galatians 2:16) - "nevertheless knowing that a man is not justified by the works of the Law but through faith in Christ Jesus, even we have believed in Christ Jesus, that we may be justified by faith in Christ, and not by the works of the Law; since by the works of the Law shall no flesh be justified."
The sanctification comes after justification. True repentance is needed for true faith, but to be saved on the idea one stopped committing a sin, not a solid foundation. Christ alone saved the damned.
In your proof text, Luke 13:3 Jesus was countering the idea that most Jews in that day had. They believed one who suffered the worst had committed the worst sins. Jesus was bringing them all onto equal ground, you too will all perish unless you repent, just like they did. He wasn't trying to define salvation.