Why can’t the Jews see that Jesus is clearly the Messiah they have been waiting for?
Blinded by Satan
The reason all people cannot believe in Jesus, including the Jews, is that until people are quickened by God’s Spirit, they are dead in their sins. In fact, the Apostle Paul says, “even if our gospel is veiled, it is veiled to those who are perishing. In their case the god of this world has blinded the minds of the unbelievers, to keep them from seeing the light of the gospel of the glory of Christ, who is the image of God” (1st Cor 4:3-4). You and I “were dead in the trespasses and sins in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience” (Eph 2:1-2), however, “God, being rich in mercy, because of the great love with which he loved us, even when we were dead in our trespasses, made us alive together with Christ—by grace you have been saved” (Eph 2:4-5). Just like Lazarus was four-days-dead and would have remained so, we could not have raised ourselves from the dead, in this case, spiritually dead, so it wasn’t until the Spirit of God revealed to us Who Jesus is and why we need the Savior that we trusted in Him. God alone calls or draws people through Christ (John 6:44), because none of us understand the gospel or even seek after God with His Spirit (Rom 3:11). This is not only the reason the Jews don’t believe in Jesus; it’s the reason that everyone who rejects Christ don’t believe. They can’t believe in the Son of God until the Father sends the Spirit of God to make them into the children of God.
An interesting fact about Isaiah 53 is that some Jews actually believe that chapter is about them, and many believe that they are the suffering servant and not Christ. Indeed the Jews have suffered enormously, but that belief doesn’t hold up when we closely examine this chapter. For example, Jesus “was despised and rejected by men, a man of sorrows and acquainted with grief; and as one from whom men hide their faces he was despised, and we esteemed him not” (Isaiah 53:3), and “he was pierced for our transgressions; he was crushed for our iniquities; upon him was the chastisement that brought us peace, and with his wounds we are healed,” (Isaiah 53:5), so it’s impossible that the Jews as a people were crushed because of our sins (iniquities) and pierced for our transgressions, but also that we are healed by the wounds of the Jews. For the Jews to believe that “the Lord has laid on him the iniquity of us all” (Isaiah 53:6b) on them, is to believe that redemption is found in the Jews…but it is found in one Man alone, Jesus Christ (Acts 4:12), and even though He was Jewish, His Jewishness had nothing to do with our being cleansed from all unrighteousness (2nd Cor 5:21). Then there is the problem of the male-gender, singular use of “He” which makes it impossible to be about a people; and the fact that it was the Jews who “bore the sin of many, and makes intercession for the transgressors” (Isaiah 53:12b). Abraham  believed God and it was accounted to him as righteousness (Gen 15:6; Gal 3:6), so faith in God existed long before the Jews even arrived, and while they were still yet in the loins of Abraham.
Jesus as Messiah
Jesus didn’t fully reveal Who He was until later in His ministry, but at one point, early on, Jesus met the Samaritan woman at the well, and “The woman said to him, ‘I know that Messiah is coming (he who is called Christ). When he comes, he will tell us all things.’ Jesus said to her, ‘I who speak to you am he’” (John 4:25-26). When Jesus was calling His disciples, Andrew “found his own brother Simon and said to him, ‘We have found the Messiah (which means Christ)’” (John 1:41). In the Old Testament, Micah wrote that “Bethlehem Ephrathah, who are too little to be among the clans of Judah, from you shall come forth for me one who is to be ruler in Israel, whose coming forth is from of old, from ancient days” (Micah 5:2). In David’s Messianic psalm about Christ, he prophesied that “dogs encompass me; a company of evildoers encircles me; they have pierced my hands and feet— I can count all my bones— they stare and gloat over me; they divide my garments among them, and for my clothing they cast lots” (Psalm 22:16-18), which we have seen take place at the cross (Matt 27:35) and the piercing of Jesus’ hands and feet was foretold hundreds of years before crucifixions ever took place. Isaiah prophesied about the coming of a New Covenant, writing, “I will give you as a covenant for the people, a light for the nations, to open the eyes that are blind, to bring out the prisoners from the dungeon, from the prison those who sit in darkness” (Isaiah 42:6b-7a), and many people received their sight, many lame began to walk, many mutes began to speak, and many dead were raised to life. And, sounding much like the first chapter of the gospel of John (1:4-8), Isaiah writes, that Christ (the Messiah) “will lead the blind in a way that they do not know, in paths that they have not known I will guide them. I will turn the darkness before them into light” (Isaiah 42:16).
Old Testament Citations
In the Old Testament, there are so many references about the coming Messiah that we cannot possibly contain them all in one article, but a few very important ones, and ones that distinctly show that Jesus is the Messiah, include Isaiah 7:14, where he wrote, “Therefore the Lord himself will give you a sign. Behold, the virgin shall conceive and bear a son, and shall call his name Immanuel,” and the name, “Immanuel” means “God with us,” and in fact, Jesus was with us, dwelling in the flesh (John 1:14). In prophesying of His coming betrayal by Judas, the psalmist prophecies, “Even my close friend in whom I trusted, who ate my bread, has lifted his heel against me” (Psalm 41:9). Of course, that happened on the night of the Passover  Meal, when Judas betrayed Jesus for thirty pieces of silver. Psalm 22 is clearly about Jesus and could never have been written about the Jewish people, mainly because Israel had yet not split into two nations yet as they would after the time of King Solomon’s reign was over, so the Jews at that time did not even exist as a people. It was only Israel.
There are so many Old Testament and New Testament Scriptures that reveal Jesus as the Messiah, it’s amazing that the Jews can’t see it. Jesus rebuked the religious leaders of His day for their blindness, and even though they knew the Scriptures, their blindness kept them from seeing Who Jesus is. The god of this world has blinded most of the world to Jesus’ true identity, but when the Spirit of God comes upon a person, they suddenly see their own sinfulness as God brings them to repentance. Then they see the desperate state they’re in without Christ, and this makes them run to the cross and put their trust in Christ. A day is coming when the Jews will finally see Jesus for Who He really is, but that day’s not today, and the same blindness that is on the Jews, which Paul calls a veil, will someday be lifted by God, so that once again, the Jews, and in fact, all of Israel alive at that time, will call upon the Lord and be saved, and then, they shall all know the Lord as the earth will be full of the knowledge of God (Isaiah 11:9; Hab 2:14).
More reading on the Messiah: Who is the Messiah? 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), Crossway Bibles. (2007). ESV: Study Bible : English standard version. Wheaton, Ill: Crossway Bibles. Used by permission. All rights reserved.