The first objection to consider is to the originality of these "I say unto you" sayings, which are presumed to be Matthew's own redactional creations - in part because the same material appears in the Lukan parallels standing on their own, without such references, thus supposedly implying they were not originally said by Jesus with the sort of implication that is described.
Concerning the exact phrase in question, however, even Fuller, who doubts that the Sermon as recorded represents the actual words of Jesus, nevertheless agrees that the phrase in question "was characteristic of the historical Jesus." [Full.FNC, 104] The consistent use of the phrase indicates that it was one of Jesus' characteristic sayings. Fuller offers this explanation of the meaning of this phrase [ibid., 105]:
Throughout his ethical teaching Jesus confronts men with the direct demand of God. In him that demand is immediately uttered. He is not reporting or interpreting a tradition, like the Rabbis. Nor is he reporting a message received from a distant God, like the prophets. God is directly present in the words of Jesus...demanding unreserved obedience to his will from those who have accepted the eschatological message and its offer of salvation.
In short, saying "I say to you" here signifies a very unique authority to speak without qualification concerning God's will. Prophets wisely prefaced their remarks with something like, "This is what the Lord says.." Jesus prefaced His remarks with "I say...", thus granting Himself the authority of God. This is either an indirect claim to divinity - or an extremely egotistical assertion on Jesus' part.
But the Jewish prophets were also sure they spoke with divine authority, though there is no reason to suppose Isaiah, Jeremiah, or Amos believed he was God.
The big difference between Jesus and the scribes, however, is that the claims of Jesus were much more audacious and self-descriptive than those of the scribes, or the prophets. This is a matter of scale, not merely certitude: The issue, is not one of certitude, but of source. The scribes always understood their dicta as ultimately deriving from Moses. They spoke with certitude (!), but not with "authority"...which is a significant difference. Lee M. McDonald writes [LM.FBC, 104]:
Jacob Neusner has also seen this tendency of Jesus to stand in opposition to the Law in the Gospel of Matthew. Neusner says that when Jesus says, "You have heard it was said...but I say to you...," he is contrasting his words with 'nothing less than the Torah, God himself speaking through his prophet Moses. Any observant Jew would immediately recognize that fact." Neusner goes on to say that in these passages Jesus is "not simply being assertive, in our modern parlance; he is claiming for himself the right to adapt, or modify, Divine Law." He then asks of Jesus, "Who do you think you are -- God?"
Jesus was only contrasted with the scribes and leaders; not with the prophets -- He consistently aligned himself with them in all his stories. This explicit solidarity notwithstanding, Jesus uniqueness relative to them lies in his:>
- being the very content of their prophecies (cf. John 5:45 and Matt. 26:56; Luke 18:31);
- non-human source of origin (e.g. John 3:31; 8:23); and,
- being the only conjunction of ALL the messianic roles: prophet, priest, king, wise man.
But, we must also keep in mind that Jesus invoked the authority of Moses and the prophets as well -- and well He could, since he himself was the spirit behind Moses (1 Pet 1:11).