Well, I can't argue that the OT had SOME degree of infulence, but to WHAT degree is still out.
Considering that at times the NT and the OT seem to be at odds over many things, I don't think the OT had THAT much influence on the message but the writers were "OT writers" in the sense that it was the OT "format" that they worked from, since it was what they had been exposed more than any other type of writing/learning.
PSacramento....On the contrary, the gospel writers (certainly in the case of the author of John who was explicit on this point, cf. John 5:31-39, 45-47, 12:41, 1 John 5:9) regarded the OT as a true and superior witness to Jesus, and thus turned to it as a principal biographical source. This involved a rather free and creative interpretation of passages in the OT, which then supplied many narrative motifs, details, and even wording and phrasing. This process is very similar to the one used by rabbis who invented stories about the patriarchs and Moses, who believed that they were discovering hidden truths in the Torah through midrashic interpretation.
So there are many features of the text that are better explained by the thesis of OT influence in narrative composition than by the alternative. For example, the Matthean and Lukan nativity narratives presume mutually exclusive scenarios and each have a bevy of narrative motifs not found in the other. There are no Magi, star, angelophany to Joseph, divorcing of Joseph and Mary, slaughter of the innocents, sojourn in Egypt in Luke, and there is no census, barren mother motif, priestly setting, Magnificat, etc. in Matthew. If you examine the intertexts and exegetical traditions involved in the two accounts, you will see that the narrative features in Matthew and Luke parallel entirely distinct sets of intertexts and traditions, the former parallels those pertaining to Moses and Luke parallels those pertaining to the prophet Sameul. While the two accounts contain some common themes, the Moses-linked material in Matthew is never found in Luke, and vice versa, the Samuel-linked material in Luke is never found in Matthew (later infancy gospels like the Protevangelium of James, on the other hand, amplifies the influence from the Samuel traditions while also mixing the two sets of motifs in harmonistic fashion). If the two writers were simply giving historical reports, there is no reason why we should find such a distribution, whereas it is neatly accounted by the fact that the authors drew on different sets of traditions (and that Luke has possibly drawn on Josephus for the historical setting). And the traditions involved are not strictly those found in the OT but those which have already been elaborated in midrashic interpretation. It is the same with the story of the wilderness temptation, which draws obviously on the wilderness wandering narratives from the OT, as elaborated in extracanonical storytelling. The two accounts of the death of Judas Iscariot in Matthew and Luke-Acts again are neatly explained by the use of different intertexts in their composition, and it is instructive that later elaboration of the story (such as that found in Papias) drew more detail from the same intertexts. Indeed the whole plot involving Judas and the arrest is explicable from a small number of OT intertexts involving King David and his betrayer Ahithophel, the sheep sold for slaughter in Zechariah (linked to the Ahithophel story by common language), and the betrayal of Joseph by his brothers. And the passion narrative has the highest density of OT exegetical traditions with many details motivated entirely by them (such as the handwashing scene with Pilate and the dialogue attributed to the crowd before him), or employed in different ways by the different writers. So to fulfill the giving of vinegar and gall in Psalm 69:21, Jesus is given wine mixed with gall before the crucifixion in Matthew 27:34 (which assimilates the older Markan reference to wine and myrrh to that in the OT intertext), he is given vinegar mixed with gall before the crucifixion in Barnabas 7:5 (which is even closer to the OT intertext than what is in Matthew, as is generally the case in Barnabas which lacks a narrative per se), whereas Jesus is given vinegar mixed with gall after he has been crucified in Gospel of Peter 5:16 (which fully assimilates the Markan reference to Psalm 69:21, with the giving of gall occurring after Jesus is nailed to the cross and not before as it is in Matthew and Barnabas).