Refuting the Christian interpretation to Bilam's Prophecy 

This week's Dvar Torah is by Rabbi Dr. Yossef Slotnick,
Rosh Kollel, Capetown (1997-1999), currently Ra”m in Yeshivat Ma'ale Gilboa

Torah Mitzion Torani Tzioni Movement

Judaism Torah Mitzion
Torah Mitzion

In our parsha we are introduced to the prophecies of Bilam. One of them is apocalyptic in nature, and is one of the only times the Torah describes a futuristic vision:
"I see it, but not now; I behold it, but not soon. A star has gone forth from Jacob, and a staff will arise from Israel which will crush the princes of Moab and uproot all the sons of Seth. Edom shall be possessed, and Seir shall become the possession of his enemies, and Israel shall triumph. A ruler shall come out of Jacob, and destroy the remnant of the city". (Bemidbar 24, 17-19)
The Christian world saw these verses as referring to their messiah. While we have no documentation of Chazal directly refuting these claims, we may still be able to discern two ways in which they did deal with the issue.

The first is by disputing Bilam's status as a real prophet. Thus the Mishna in Sanhedrin states that Bilam has no place in The World to Come. The Mishna in Masechet Avot also counter juxtaposes Bilam and Avraham as diametric opposites:
Whoever possesses the following three traits is of the disciples of our father Abraham; and whoever possesses the opposite three traits is of the disciples of the wicked Balaam. The disciples of our father Abraham have a good eye, a meek spirit and a humble soul. The disciples of the wicked Balaam have an evil eye, a haughty spirit and a gross soul. What is the difference between the disciples of our father Abraham and the disciples of the wicked Balaam? The disciples of our father Abraham benefit in this world and inherit the World To Come, and as is stated, "To bequeath to those who love Me there is, and their treasures I shall fill". The disciples of the wicked Balaam inherit purgatory and descent into the pit of destruction, as is stated, "And You, G‑d, shall cast them into the pit of destruction; bloody and deceitful men, they shall not attain half their days. And I shall trust in you" (ibid., 55:24). 
Once can assume that the emphasis on the students and Bilam and Avraham is meant to show the difference between them continuing till this day and age. I also accept the claim of the 19th century researchers, that occasionally Chazal equate Bilam to the Christian messiah.
Another example can be found by comparing midrashim over time - In early, Mishnaic, midrashim Bilam's prophecy is described as greater even the Moshe's himself. In the later, Amoraic midrashim he is perceived as at a lower level even than the other prophets in the Tanach.
It would seem that to the extent that Chazal belittle Bilam's stature, so too his prophecies have less weight. Thus the 'proof' the Christians bring from him are no longer relevant.
A second approach in Chazal does not ignore the importance and relevance of Bilam's prophecy, but rather puts in his mouth an additional prophecy (based on the existing texts), which clearly refutes the Christian messiah:
 Rabbi Elazar HaKapar said: G-d gave (Bilam's) voice strength and it was heard from one end of the earth to the other. He (Hashem) saw the nations worshipping the sun, the moon and the stars, to (statues) of wood and stone.
And he foresaw that a man, son of a woman will rise and claim he is a god (to) mislead the entire world… and he said: 'Take heed not to be misled by that man, for it says "G-d is not a man that He should lie" (Bemidbar 24, 19), and if he claims he is god he is lying.
And he will claim he is the son of god, while he is truly the son of a man, as it says (ibid, ibid) "…nor is He a mortal that He should relent"…
And he ends and says "Alas! Who can survive these things from God? " (ibid, 24, 23) – who will live from the nations who followed a man who made himself a god?
The midrash clearly describes and discredits the Christian theology. At the same time they recognize the stunning success of Christianity in spreading throughout the world. Against this Bilam tells the world "G-d is not a man that He should lie". Any man who claims he is god is lying! The Bilam of the midrash is aware his warning will go unheeded as cries "Who can survive these things?". It is very likely this interpretation of Bilam's prophecy is meant to counter the Christian interpretation of one of Bilam's other prophecies; "G-d in not a man"!