To begin with letís look at where the Bible says repenting is necessary. Jesus Himself calls us to repent as shown in Mark 1: 14-15 Now after John was arrested, Jesus came into Galilee, preaching the gospel of God, and saying, "The time is fulfilled, and the kingdom of God is at hand; repent, and believe in the gospel." Even after the death and Resurrection of Christ the call for repentance is still carried on as shown in Acts 3:19 Repent therefore, and turn again, that your sins may be blotted out, that times of refreshing may come from the presence of the Lord. We believe that our sins must be blotted out for us to obtain Salvation, and this passage clearly indicates a need to repent to have sins blotted out. Since this took place after the death and Resurrection it can not be argued that Christ's death and Resurrection is sufficient to grant Salvation.
There is other Biblical evidence that indirectly shows repenting is necessary. To receive the Holy Spirit we must repent as illustrated in Acts 2:38 And Peter said to them, "Repent, and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins; and you shall receive the gift of the Holy Spirit.(") Repenting also is pleasing to God. When the apostles preached repentance God showed favor to them as shown in Mark 6:12-13 So they went out and preached that men should repent. And they cast out many demons, and anointed with oil many that were sick and healed them.
While often overlooked as something necessary to achieve Salvation, Scripture clearly shows that repenting is necessary. Scripture is filled with direct calls to repent. Scripture also shows that repenting is pleasing to the Lord. It is for these reasons that repentance is necessary.