@John Aquila
Jews have a totally different understanding of that text from Daniel. We don't even include Daniel as one of the books of the prophets, even though he was a prophet himself. The text in Daniel 9 reads differently in the Hebrew, and this makes the formula something different for us. We read it as discussing 70 years of Babylonian exile followed by 420 years of the Second Temple.
Not all Jews see prophecy about the Messiah as referring to a literal person. Many Jews see these prophecies as referring to a Messianic Age. Also the term "messiah" in Hebrew just means someone who has been chosen to rule, often being marked by literal anointing with oil as a sign of their installation. Because of that the references to "moshiach" in Daniel 9 have often been interpreted to be Cyrus, King Agrippa, and the High Priest at the Temple at the time of its fall is the third "moshiach." The term just means "anointed one" as in a ruler or priest.
It should be noted that the New Testament authors never quote this text or offer the general formula popular among Christians for Daniel chapter 9 in connection with an expected arrival of the Messiah. Being independent of the New Testament, the formula and its final conclusions are not directly based on any Christian Scripture.