Psalm 83 (Made for Israel)
Why is Israel given the status of God's chosen nation? It has nothing to do with what Israel has done to deserve this status and everything to do with God's grace. Through a form of sovereign election, God elected to choose Israel for a unique, special mission to the rest of the world. Israel was the receiver and keeper of God's word until it could be shared with all nations. Once the Messiah came though Israel's bloodline, the entire Bible went out to all nations fulfilling the promise/prophecy God made to Abraham when He said In your seed all the nations of the earth shall be blessed (Genesis 22:18).
For more on this please read Israel The Chosen Nation.
Israel still has a specific role to play in End Time Prophecy. Although Israel has been a nation that has not always listened to God, she will always be the apple of God's eye. Israel receives her blessings through grace and grace only. It is the same for those who have faith in Jesus Christ as Messiah. Through God's grace we are saved, not because of something we have done (other than faith) but because God elects to make it that way. That's why Abraham's faith was credited towards him in the form of righteousness and not his works (Genesis 15:6). Through the Messiah we are saved by faith, not by works. For more on Israel's prophetic role please go to Israel In End Time Prophecy.
There are organizations inside Israel that are promoting the re-building of the Temple on the Temple Mount. The progress of the construction process concerning the utensils that will service the Temple has already started. To track this progress please go to Rebuilding The Temple.
The question is really much bigger than that. The answer is not that Israel needs the Gospel but that the world needs the gospel which Israel is a part of.
Israel is certainly in a unique situation being God's chosen nation. However, Israel needs all the blessings that God has in store for her and that includes knowing her Messiah and King. Prophecies like Zechariah 12:10 and Zechariah 14:1-7 teach us that in the end Israel will recognize her Messiah, just before His second coming to earth. We are given a glimpse of the heart of Paul in the book of Romans. This should be the heart of all people who love Israel.
There are now many organizations that are dedicated to Bringing The Gospel To Israel and helping the Jews to learn about the New Testament. Many have no idea that the New Testament was written by mostly Jewish authors, the same as the Old Testament. Others have no idea that God promised Jeremiah that some day there would be a New Covenant (Jer. 31:31). Although this New Covenant is here now it will take the return of Jesus to be fully implemented. For more on Israel needing the gospel please read Is Judaism A False Religion?
There is no substitute for a trip to visit Israel.
Read about The Messiah.