Viewing v. 38 in light of vv. 22-37, we conclude that "the Pharisees and teachers of the law" want a sign (1) which is not subject to the interpretation the Pharisees have placed on Jesus' exorcisms, v. 24 (Gundry, 242), (2) which Jesus himself does not originate, lest it remain subject to that same charge (Tasker, 131), and thus (3) which clearly originates with God: cf. 16:1, where the Pharisees and Sadducees "tested [Jesus] by asking him to show them a sign from heaven."
The Sign of Jonah. 12:39-40.
The term sameion. This noun (v. 39, v. 38) has an unfavorable sense in the Synoptics (though favorable in Jn). Here it refers to an act so stupendous as to leave no room for doubt - or for faith. It is the kind of act that Satan tempted Jesus to perform, 4:6. Such a request shows the wickedness and infidelity of Jesus' generation (on "adulterous" as signalling unfaithfulness to God, see the references in Gundry, 243).
Identifying the sign, v. 40. V. 40a corresponds exactly to Jonah 1:17. Concerning v. 40b, Gundry comments (240):
"The heart of the earth" "does not refer simply to a grave, but means the realm of the dead...and alludes to Jesus' death."
"Jesus stayed in the realm of the dead parts of three 24-hour periods, not three whole days and nights. But the reference to three days and three nights comes out of Jon 2:1 [1:17] rather than from the story of Jesus and causes no problem in view of the Jewish method of reckoning part of a 24-hour day for the whole."
"Here is the only reference to his death and resurrection that Jesus made in the hearing of Jewish leaders."
Interpreting the sign. In accord with the demand of v. 38, Jesus speaks of a sameion accomplished by God (cf. the passive "be raised" in 16:21). But Jesus does so in a highly allusive way: his resurrection is stated implicitly (v. 40 implies that he will be in the heart of the earth only three days and nights), not explicitly (contrast 16:21, addressed to "his disciples"). Moreover, according to the NT no one (not even an apostle, much less a Pharisee) witnessed the resurrection itself, but only appearances of the risen Jesus. In other words, while the resurrection was to be a stupendous miracle, one which could be explained only as a direct act of God, even it would not exclude the need for faith. Access to the resurrection would depend on its being proclaimed by Jesus' chosen witnesses, and believed by those who hear. This leads to the next point.
The Primacy of Preaching. 12:41-42.
In the time of preparation. The Ninevites "repented at the preaching of Jonah," without the slightest knowledge of Jonah's sojourn in and deliverance from the fish. (Jonah is "the prophet," v. 39.) Likewise the Queen of the South came "from the ends of the earth to listen to Solomon's wisdom"; she was not lured to Jerusalem by stories of heaven-sent signs (except for 2 Chr 7:1-3, the OT speaks of none such during Solomon's reign).
In the time of fulfillment. The critical question is how Jesus' contemporaries respond to his proclamation. The demand for a "sign" leaves no room for faith. (Even Jesus' chosen dynameis, 11:20, are not isolated phenomena but are intelligible only in the context of the preaching of the dawning Kingdom, 4:17, 23; 11:2-6. This is what distinguishes them from mighty works during the time of preparation and thus places the witnesses under severer judgment.) The Ninevites and the Queen of the South will one day rise from the dead to face the Final Judgment; and when they do, they will condemn this generation. (Some suggest that the verbs of vv. 41a and 42a be understood in the sense of "stand to dispute, to accuse," i.e. to offer evidence for the prosecution; thus NEB. But the use of egerthasetai in v. 42 [instead of anastasontai, as in v. 41], together with the fact that the theme of resurrection has been introduced in v. 40, favor taking both verbs in the sense of resurrection; thus NEB mg., Gundry 246.) The argument is like that of 11:20-24. The OT listeners indeed responded to God's Word through his prophet; but "now one greater than Jonah [and Solomon] is here" (vv. 41b, 42b; cf. the comments on 12:6). Whereas the words of Jonah and Solomon were preparatory, Jesus' are final. And whereas Jonah and Solomon spoke with a derived authority, Jesus speaks with inherent authority (cf. 7:29; Mt's identification of Jesus as a New Moses; and prior discussion passim). Thus Jesus' listeners incur the greater judgment.
THE PERIL OF A PARTIAL RESPONSE. 12:43-45.
Cf. Joachim Jeremias, The Parables of Jesus, 197: "When an evil spirit [a Jewish synonym for "demon," cf. v. 22, daimonizomenos] comes out of a man, it goes through arid places [the natural abode of demons] seeking rest and does not find it ["since he can only be satisfied where he can wreak destruction," ibid.]. Then it says, 'I will return to the house [oikos; cf. oikia, vv. 25, 29, and Beelzeboul, vv. 24, 27] I left.' When it arrives, it finds the house unoccupied, swept clean and put in order [i.e., "prepared for the ceremonious reception of a guest," ibid.]. Then it goes and takes with it seven other spirits more wicked than itself ["seven is the number of perfection; the seven evil spirits represent every form of demonic seduction and wickedness"], and they go in and live [katoikei, present tense] there."
Taking account of links with 12:22-37 and 12:38-42 (see above), we conclude that Jesus is warning of the great peril of dissociating the exorcisms from his ministry as a whole. Even if one is convinced that he casts out demons by the Holy Spirit (v. 28), such a realization is by itself inadequate, and must be joined with acceptance of his preaching of the Kingdom and commitment to his person. "The house must not remain empty when the spirit hostile to God has been expelled. A new master must reign there, the word of Jesus must be its rule of life, and the joy of the Kingdom of God must pervade it" (ibid., 198; cf. T. W. Manson, The Sayings of Jesus, 88).
THE NEW DIVISION. 12:46-50.
People are divided according to the way they respond to the testimony of Jesus; cf. 10:34-38. Jesus does not (in 12:48-50) exclude his earthly family from the kingdom of heaven - just as 11:11 did not exclude John. Rather, Jesus is declaring in the starkest terms that (i) the kingdom of heaven is a greater reality than the strongest earthly ties (again 10:37-38), (ii) the citizens of the kingdom of heaven comprise a genuine family (under "the Father in heaven"), and (iii) the members of the kingdom are those who do the heavenly Father's will (cf. 7:21).