"O foolish Galatians...!" -- Paul, Galatians 3:1
Paul has stern words for any Christian who thinks we are receive eternal life by loving God or loving our neighbor (the twin pillars of the Law). He calls them "foolish." He also calls them "bewitched", and disobedient to the truth.
Why such strong language?
First, it's because the idea that we hang onto our salvation by law-keeping shows a terrible ignorance of Christ's death the cross (v. 1b). Christ's death on the cross paid the price for every time we fail to love God or neighbor. God's standard is perfection. If you say that we receive eternal life by loving God and neighbor, then you must also say that we must love God and neighbor perfectly. Anyone knows that this is impossible to do.
Did the Law offer everlasting life? Yes, indeed it did. It offered everlasting life on the condition of perfect performance. Christ made this clear in his talks with the rich young ruler, and with the scribes. "What must I do to inherit everlasting life?", the young ruler asked. "Keep the commandments," Jesus replied.
Did the young ruler go on to ask Jesus, "Teacher, do I have the ability to keep the commandments"? No, that question was never asked. But if the young ruler had asked Jesus that question, Jesus' answer would have been "No, you cannot."
The cross was necessary, because a lost sinner cannot love God or his neighbor perfectly, and a saved sinner cannot love God or his neighbor perfectly. So, when someone says that we must keep the law in order to inherit eternal life, we are hearing deep ignorance of sin's power and a deep, fundamental miscomprehension of the cross.
Paul says no one receives the Holy Spirit by law-keeping (3:2). God gives the Spirit only to those who have trusted in Christ. "Come to Me, all of you who thirst," Jesus said on the last day of the feast, "And I will give you living water, which will spring up inside you unto everlasting life!" Jesus never said, "Come to me, and keep the commandments, and I will give you the Spirit."
You must choose between believing in the cross, or believing that we keep the law in order to inherit everlasting life. Paul says, if we must keep the law in order to be justified of our sins, then Christ died in vain (Galatians 2:21).
It is right to say that the holy fruit in our lives shows our faith in the cross. It is wrong to say that the holy fruit in our lives is something we must do above-and-beyond trusting in the cross. The first is the Gospel. The second is heresy.