Just as Jonah was in the belly of the fish three days and nights (Jonah 1:17), so also the Lord will be in the belly of the grave for a similar period of time. However, just as Jonah was rescued by God from the fish so he could accomplish his mission (Jonah 2:9-10), Jesus will be saved from the grave to accomplish his mission. Jesus therefore indicates the great sign which will be given by His Father so nonbelievers will finally be able to believe.
Jesus goes not to castigate those who are unwilling to listen to him without this greatest sign. He points out how the Queen sought wisdom by seeking one known to be wise. This required much effort on her part and as such demonstrates the truth of scripture (cf. Wisdom 7) but the present generation will not listen.
Jesus returns to the example of Jonah who preaches to non-Jews who had no reason to listen and believe his warning but they did and were saved (Jonah 3). Jesus' listeners are Jews and leaders among the Jews, but this people will not listen and therefore are lost. In this He is predicting that even after the greatest sign most of them will resist.