3 In the time then of the Old Testament, brethren, the promises from our God to that carnal people were earthly and temporal. There was promised an earthly kingdom, there was promised that land into which they were also led, after being delivered from Egypt: by Jesus son of Nave they were led into the land of promise, where also earthly Jerusalem was built, where David reigned: they received the land, after being delivered from Egypt, by passing through the Red Sea....Such were also those promises, which were not to endure, through which however were figured future promises which were to endure, so that all that course of temporal promises was a figure and a sort of prophecy of things future.
Accordingly when that kingdom was failing, where reigned David, the son of Jesse, that is, one that was a man, though a Prophet, though holy, because he saw and foresaw Christ to come, of whose seed also after the flesh He was to be born: nevertheless a man, nevertheless not yet Christ, nevertheless not yet our King Son of God, but king David son of Jesse: because then that kingdom was to fail, through the receiving of which kingdom at that time God was praised by carnal men; for this thing alone they esteemed a great matter, namely, that they were delivered temporally from those by whom they were being oppressed, and that they had escaped from persecuting enemies through the Red Sea, and had been led through the desert, and had found country and kingdom: for this alone they praised God, not yet perceiving the thing which God was designing beforehand and promising in these figures.
In the failing therefore of those things for which the carnal people, over whom reigned that David, was praising God, “there failed the hymns of David,” not the Son of God, but the “son of Jesse.”...
Source: The Enarrations, or Expositions, on the Psalms (New Advent)