“Scripture would have us conclude that Jews are not saved....”
“However, let me bring in another wrinkle- it is not only that Jews reject Jesus, but they clearly reject the resurrection of the body. “
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Jews do not reject the concept of resurrection - in fact, Christianity adopted the idea from Judaism.
What Judaism and believing Jews reject is the idea that Jesus was the Messiah according to the criteria set forth in the Bible: http://jewsforjudaism.org/knowledge/articles/answers/jewish-polemics/the-jewish-messiah/messiah-the-criteria/
As for the “Jew are not saved” part, that is according to the Christian Bible, which is not something that Jews believe in (for reasons stated in the article cited above). According to the 5 Books of Moses and the Oral Law given by G-d to Moses on Mt. Sinai, each individual (Jewish or not, just so you know, because Judaism is NOT the exclusive means of attaining a place in the World to Come, i.e. Heaven) succeeds or fails in their quest to improve their soul via their acts here on Earth. You are not “saved” merely by belief - it requires acts that confirm that belief. For non-Jews, the path to such improvement is via abiding by the 7 Noahide laws. http://www.aish.com/w/nj/For_Non-Jews.html
The New Testament book of Romans, written by Paul, very systematically deals with Jews and their system of law, and Gentiles, in relation to salvation.
Gentiles are dealt with first in chapter 1. Their paganism is utterly condemned. Jews are dealt with next, they “make their boast of God...being instructed out of the law are confident they are a guide to the blind, a light to them which are in darkness. An instructor of the foolish, a teacher of babes,” 2:17,19,20.
But, even though Jews have the law, they have not kept it. The situation of both Gentiles and Jews being summed up by saying: “We have proved both Jews and Gentiles, that they are all under sin. There is none righteous, no, not one” 3:9,10 Jews are as much sinners as the pagan Gentiles.
Whats the answer to this sad situation? “The righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: FOR THERE IS NO DIFFERENCE. FOR ALL HAVE SINNED, AND COME SHORT OF THE GLORY OF GOD.” 3:22,23.
So, yes, according to Romans, “the Vatican is wrong, Jews do need Jesus for salvation.” Likewise, yourself, and all Jews.
Christ said, “I am the way, the truth, and the life, NO MAN - which means all men, including Jews - cometh unto the Father, but by me,” John 14:6. Whether Jews or Gentiles, faith in Jesus Christ is the one and only way to God.