Is this idea propagated in the New Testament? Yes, it is.
Romans 6:1-4 (NKJV)
"1 What shall we say then? Shall we continue in sin that grace may abound? 2 Certainly not! How shall we who died to sin live any longer in it? 3 Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death? 4 Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life."
"1 What shall we say then? Shall we continue in sin that grace may abound? 2 Certainly not! How shall we who died to sin live any longer in it? 3 Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death? 4 Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life."
Although all of our sins are covered in Christ, past, present, and future; it is expected that we not continue in a life of sin. We have been saved from death to live a new life, a life in Christ, a life characterized by His righteousness and His example.
Beloved you are free from sin. Live no longer in it.