There are two major, conflicting, ways to understand this verse. First, this hardening in no way rejects human responsibility. Israel had consistently been confronted with being born from above and consistently rejected it. Unbelief is not blamed upon a harsh, predestinarian God, but is portrayed as a punishment. This punishment takes the form of abandoning them in their unbelief “as a result of which whatever God gives them to see and hear can no longer lead to salvation, that is, to repentance and healing” (so Ridderbos, 444-45).
The second way views the original Isaiah text as a use of irony. Hollenbach is the major promoter of this view. First, Hollenbach defines irony as “an expression of scorn directed against someone made by the speaker taken at face value.” The problem with irony is that, especially in English, there is no way to communicate it in the text. Therefore, context remains determinative in deciphering where irony exists.
Hollenbach says, “Isaiah 6.9, 10a serves largely to characterize the audience to which Isaiah’s message will be directed.” It was not that Isaiah was told to command them to be hardened (as the Hebrew text appears to indicate) but that he was told that they would be hardened (as the LXX appears to indicate). It appears, then, that the translators of the LXX were making the irony more explicit. This can also be seen in Matt 13:15 and Acts 28:27, in which they say, “they have closed their eyes.” Therefore, it was the people who rejected God. “John 12:40a basically quotes Isaiah 6.10a to show that the whole of Jesus’ ministry was prophesied by Isaiah to effect stubborn unbelief.” Since Jesus is the subject in 12:40, it would be him who was blinding the people. This makes his appeal in 12:35–36 seem disingenuous. Hollenbach concludes that the most plausible way of understanding Isa 6:10b (and John 12:40b) is as a statement of irony “showing God’s disgust with the unwillingness of his people to respond to Him.” If that is true, then the attitude of God toward his people in Isaiah is parallel to Jesus’ attitude toward the crowd in 12:35–36: “although time is running out, they are reluctant to respond.” According to Hollenbach, this verse is used by the Evangelist to explain why the crowd did not want to repent.
Both of these views have much to merit them, but since the evidence for Johannine irony has been mounting in recent research, Hollenbach’s argument has more to favor it. With this understanding, the theme of believing and repentance have come to the front as the themes for this passage.
Against this, it could be argued that the mentioning of strefo is inconsequential to the argumentation of this passage (especially if the first view is taken) and that the author of the FG is not, himself, using the word, but he is just quoting the Isaiah passage. In response to the former, 12:39 and Hollenbach’s hypothesis argue against strefo being an inconsequential word in this passage. This verse frames the discussion into a salvific context by the use of “believe.” The argumentation is as follows: “The Jews refused to believe and repent and have hardened their minds and eyes to the signs of Jesus.” The inclusion of the statement in 12:42 that nevertheless many believed gives an “implicit appeal to believe” to 12:37–40. The closing words of John 12:40 discuss “turning” and “healing.” Taken as irony, these words are a condemnation to the Jews who have hardened their hearts and blinded their eyes because they did not want to repent and be healed. The latter argument, that the author of the FG is not actually employing the term himself, is a little hazy. While it is true that the FG is referring to Isa 6:10, it is not a quote from the Hebrew nor the LXX. The LXX used a different (though definitely related) word; the Hebrew has many differences from this reference, also. Therefore, the author of the FG is probably reciting the verse from memory, paraphrasing it for convenience, or making the original authorial intent (irony) clearer. Regardless, it is his own words, not a slavish copying of Isa 6:10, that occurs in John 12:40. This makes his use of strefo even more compelling.
 Hollenbach, “Lest they should turn and be forgiven: Irony,” Bible Translator 34 (1983): 312–21. The following discussion is heavily dependent upon his article.