The controversial statements by Alan Chambers and the criticism by Robert Gagnon rehearse age-old issues that Christians have wrestled with since the beginning: What exactly is the place of works after one is saved? What difference do they make, if any? I've been asked to respond from a Wesleyan Arminian point of view.
It is one of the most basic tenants of Wesleyan Arminian theology that salvation is not complete at the new birth (or justification). The Wesleyan Arminian stresses that in fact there are three tenses to salvation for the believer—"I have been saved (the new birth), I am being saved (sanctification), and I shall be saved to the uttermost (glorification)." The Arminian does not believe that a person who has only experienced the new birth has completed the salvation process, or that the rest of the process is inevitable and foreordained. Nor does the Wesleyan Arminian believe that the behavior of Christians subsequent to conversion is irrelevant to whether or not they are being sanctified presently, or will be saved to the uttermost eventually.
Put in Pauline terms, it is perfectly possible for a person to experience the grace of God in the form of the new birth, and not end up in the Kingdom of God, or heaven for that matter. I like to put it this way: You are not eternally secure until you are securely in eternity, and this of course stands at odds with the fundamental Reformed position on this matter. In sum, Wesleyan Arminians believe that immoral behavior or apostasy subsequent to conversion can affect one's holiness, one's sanctification, and one's eventual glorification negatively. One cannot save one's self by certain patterns of behavior but one can certainly impede or even destroy one's relationship with God through sin whether moral or intellectual sin. God's saving grace and forgiveness is not cheap grace, and it does not rule out such a possibility. Furthermore, it seems reasonably clear to Wesleyan Arminians that this was the view of both Jesus and Paul. Let me illustrate.
Jesus, as it turns out, has quite a lot to say about believers being in danger of going to hell. In the Sermon on the Mount, we have pronouncements like "unless your righteousness [and here Jesus is clearly not talking about imputed righteousness, he is talking about the character of his disciples themselves] exceeds that of the scribes and Pharisees you shall never enter the Kingdom of heaven" (Matthew 5:20). He goes on to warn that if one insults a brother or sister by calling them a fool, he is liable to hellfire (5:22). Jesus also warns that the gate is narrow into the Kingdom of God, not because God's grace is limited, or God has chosen only a few to enter, but precisely because people choose the easy way in life when it comes to their behavior (Matthew 7:13-14)
The two-ways discussion in early Judaism was always about a choice between one course of behavior, to be avoided, and another to be embraced (see many examples in Proverbs). Jesus' advice is no different on this score. In Matthew 7:21 Jesus goes on to stress that it is not those who merely call Jesus Lord who will be saved, but those who do the will of the Father who will enter the Kingdom. Why were some turned away? Matthew 7:23 tells the tale—because they were doers of evil.
Again, the Sermon on the Mount was Jesus' teaching for those who were already Jesus' disciples, and undoubtedly the First Evangelist intended this same teaching to be a guide for his own Christian audience. Jesus was not into making idle threats that could never possibly become real penalties. Read again the parable of the sheep and goats in Matthew 25. While good behavior is not enough to get one into the Kingdom of God, it is perfectly clear that bad behavior by disciples of Jesus can certainly keep them out of it.