The New Covenant and The Kingdom

The Jewish leaders of Jesus day were teaching and looking for a Messiah that would come and restore national Israel as the Kingdom of God on earth. They knew the time frame for the coming of the Messiah and where the Messiah would be born. How could they possibly miss the Messiah that was born in Bethlehem and came to them teaching about the Kingdom of God? The veil of Moses hid their ability to recognize Jesus as the Messiah because they had a different expectation for the Kingdom of God. Later, the Jews persecuted the Christians because they were preaching a Kingdom of God that was contrary in nature to traditional Judaism’s interpretation. The inspired NT authors removed the veil of Moses from the traditional Jewish understanding, revealing the true nature of the Kingdom.

Does that same veil of Moses hide the nature of the Kingdom of God today? Which interpretation of the Kingdom does the church more closely reflect today - the teaching of Jesus and the NT authors, or the traditional Jewish concept?