Of what happens when someone tries to hold on to the Old Testament instead of accepting that it is fulfilled and done away with the New Testament.

My faith in Jesus doesn't stem from the fact that he was prophesied in the Old Testament.

Rather, my acceptance of the OT prophets depends on the fact that they did prophesy of Jesus and that Jesus did say their prophecies came from God.

Without Jesus I would not have any interest at all in the OT pqrophecies.

The only thing that makes the Hebrew culture special in any way is Jesus.

I don't worry about exactly "how" Jesus fulfilled each and every one of the OT prophecies.

He said that he did fulfill them, and that's enough.

Mt 5:17 ¶ Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil.
18 For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.

Now what did Jesus mean by "the law" in that passage?

Animal sacrifice?

Yes. Jesus was the once-and-for-all fulfillment of animal sacrifice, the passover lamb slain from the foundation of the earth. He fulfilled the prophecy and the law.

Temple Worship?

Yes, Jesus is the true "Spiritual" temple. Destroyed and rebuilt in three days as He promised. He fulfilled the prophecy and the law.

Punishment for sins?

Yes, Jesus took the legal punishment for all our sins. He fulfilled the law.

The law has all been fulfilled in Jesus.
Prophecy has all been fulfilled in Jesus.

We mortals have yet to see the fulfillment of certain specific endtime prophecies because, as creatures of time, we are not capable of seeing the future (physically). But we can, like Abraham, see it by faith, and be persuaded of it and embrace it. In realtime (God's eternal now) those prophecies have all been fulfilled already (since the foundation of the earth in fact) in Jesus.

As far as the "David" prophecy you mentioned is concerned, Jesus is the fulfillment of that too.

As Jesus himself pointed out, contrary to a popular misconception, Jesus is NOT the Son of David, He is David's Lord.

Mt 22:42 Saying, What think ye of Christ? whose son is he? They say unto him, The Son of David. 43 He saith unto them, How then doth David in spirit call him Lord, saying, 44 The LORD said unto my Lord, Sit thou on my right hand, till I make thine enemies thy footstool? 45 If David then call him Lord, how is he his son?

Jesus fulfilled the prophecy of David, because that prophecy was not about David, it was about Christ. David was just a very imperfect foreshadow of Christ. A cartoon character depiction of how Christ rules on His throne.

For those who want to stumble, there are many prophecies that could be used as stumbling blocks.

For example, the prophecy that Christ would be called Emmanuel.

"Oh dear, but Jesus wasn't actually named actually named "Emmanuel" by his parents, so does that mean He isn't the messiah???

No, it just means some people have a misunderstanding about how the prophecy would be fulfilled.

Over the centuries many millions of people have called Jesus Emmanuel, in songs, in prayers, in sermons...
The prophecy is fulfilled.

Concerning your belief in a future awakening of the Jews and a mass conversion to Christianity.

Why not now?
Jews are totally free to awaken and convert any time they like. The blindness that is upon them is there because of unbelief, and only belief can ever take it away.

The blindness will only leave AFTER they believe.
Not before.

Ro 11:20 ... because of unbelief they were broken off,... 23 And they also, if they abide not still in unbelief, shall be graffed in: for God is able to graff them in again.

The idea that God blinded them purposely to keep them from seeing the truth is total blasphemy.

Look at the day of Pentacost. Thousands of Jews could see the truth. They weren't blind. And over the centuries millions of Jews have seen the truth. They weren't blind, because they believed.

It is Orthodox Judaism itself which insists on imposing that blindness to the truth of Christ as a condition for being Jewish. If a Jew believes in Jesus, he is immediately no longer even considered to be Jewish by the Orthodox Jewish religion.

"In brief: No Jew accepts Jesus as the Messiah. When someone makes that faith commitment, they become Christian. It is not possible for someone to be both Christian and Jewish."
Why Jews do not believe in Jesus
http://judaism.about.com/library/3_askrabbi_c/bl_jesus.htm

http://www.messianic-racism.mcmail.com/mr/rac/federow.htm

http://www.daniellerice.com/MessianicJudaism.html

http://www.chabad.org/library/article.asp?AID=42624