Narkissos....That text, from the Matthean Sermon on the Mount, is also critically informed by the following statement from the conclusion, which is perhaps most explicit in its allusion to Pauline Christianity, as it refers to those who call on Jesus as "Lord, Lord" (cf. Romans 10:9, 13; 1 Corinthians 7:10, 12, 12:3), who prophesy and perform works in his name (cf. Romans 12:6; 1 Corinthians 12:9, 28-30, 13:9, 14:5, 24, 31-39), and who view themselves as not under the "Law" (cf. Romans 3:28, 6:14-15, 7:4-6, 10:4; cf. Romans 3:31, responding to the allegation that he nullifies the Law):
"Not everyone who says to me, 'Lord, Lord,' shall enter the kingdom of heaven, but he who does the will (i.e. justification by works, not faith) of my Father who is in heaven. On that day, many will say to me, 'Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?' And then I will declare to them, 'I never knew you, depart from me, you workers of lawlessness (anomia)." (Matthew 7:21-23)
Among the Jewish Christians who believed that Jesus came to deliver new halaka to interpret the old Law (cf. Matthew 16:19, 18:18), for the Pharisees and scribes had hidden the original heavenly "keys of knowledge" which gave heavenly authority to interpretations of the Law (cf. Matthew 16:19, Gospel of Thomas 19:1-2), salvation did not come through faith alone (cf. James 2:14-23). Matthew, which represents the Jewish Christian point of view, emphasizes the importance of doing the "will of the Father" (cf. Matthew 6:1-18, 12:50, 16:27), and the same can be found in the Jewish-Christian gospels, such as the Gospel of the Nazoreans 6:1, which reads: "If you are in my bosom and do not do the will of my Father in heaven, I will cast you out of my bosom". There is an interesting parallel to Matthew 7:21-23 and the Gospel of the Nazoreans in 2 Clement, which depends on non-canonical gospel material:
"Let us, therefore, not just call him Lord, for this will not save us. For he says, 'Not everyone who says to me, 'Lord, Lord,' will be saved, but only the one who does what is right.' So then, brothers, let us acknowledge him in our actions by loving one another, by not committing adultery or slandering one another or being jealous, but by being self-controlled, compassionate, and kind. And we ought to have sympathy for one another, and not be avaricious. By these actions let us acknowledge him, and not by their opposites. Further, we must fear more not men but God. For this reason, if you do not do these things, the Lord said, 'If you are gathered with me in my bosom, yet you do not keep my commandments, I will throw you out and will say to you: "Depart from me, you workers of iniquity (anomia)." (2 Clement 4:1-5)
This appears to harmonize the Jewish-Christian perspective reflected in Matthew and the Gospel of the Nazoreans with that of Paul, who apparently did explicitly claim that "everyone who calls on the name of the Lord will be saved ... If your lips confess that Jesus is Lord ... then you will be saved" (Romans 10:9, 13). The harmonization interprets the "commandments" or "will of the Father" as relating to Christian morality and not specific observance of the Law.
The perspective in Matthew 7:21-23, incidentally, radically departs from that in Mark 9:38-40 which stresses unity and not division among the followers of Jesus: "John said to him, 'Teacher, we saw a man casting out demons in your name, and we forbade him, because he was not following us.' But Jesus said to him, 'But do not forbid him; for no one who does a mighty work in my name will be able soon after to speak evil of me. For he that is not against us is for us." The Matthean Jesus however has almost the opposite opinion -- he has such followers "depart" from him, creating a division between such "lawless" ones and his own "lawful" followers. Q/Luke 6:46-49 also reveals what the original text was before its Matthean expansion into Matthew 7:21-27; it has turned a mild admonishment into a harsh condemnation by drawing on a quite different logion in Q/Luke 13:24-27.
As for the meaning of Matthew 24:12, I think it refers to persecution from both Pharisees and former Christians (thus "betraying" their former friends, v. 10), who in the Jewish-Christian context of the gospel are those who have returned to Pharisee Judaism and thus take part in the expulsion of Christians from synagogues, previously described in Matthew 23:34: "Some of them you will kill and crucify; others you will flog in your synagogues and pursue from town to town." This fact is clear from the parallel between 24:9-13 and 10:17-23 (as well as 23:34)
"Then they will deliver you up to tribulation, and put you to death; and you will be hated by all nations for my name's sake. And then many will fall away, and betray one another, and hate one another. And many false prophets will arise and lead many astray. And because lawlessness is increased, most men's love will grow cold. But he who endures to the end will be saved" (Matthew 24:9-13).
"Beware of men, for they will deliver you up to councils, and flog you in their synagogues, and you will be dragged before governors and kings for my sake....Brother will deliver up brother to death, and the father his child, and children will rise up against parents and have them put to death; and you will be hated by all for my name's sake. But he who endures to the end will be saved. When they persecute you in one town, flee to the next; for truly, I say to you, you will not have gone through all the towns of Israel before the Son of Man comes" (Matthew 10:17-18, 21-23).
"Woe to you, scribes and Pharisees, hypocrites! ... I send you prophets and wise men and scribes, some of whom you will kill and crucify, and some you will flog in your synagogues and persecute from town to town" (Matthew 23:29, 34).
As you can see, the three texts are connected to each other by shared themes and phrasing. So I think the reference to "love growing cold" is likely that of those who defect from Jewish Christianity back to Pharisee Judaism and take part in the Pharisee persecution of Christians at the beginning of the second century A.D. However, I do agree too that the reference to "false prophets" and anomia in Matthew 24:11 is possibly oriented to Pauline Christianity as well, considering the linkage betwen "prophecy" and anomia in Matthew 7:21-23. It is possible that the author is criticizing both extremes, e.g. those who no longer follow the Law and those who follow it in the wrong way and persecute the disciples of Jesus.