Several hundred years after God drafted the covenant with the Jews, Jesus came to earth to draft and ratify a broader covenant with the entire human race. The principals of this covenant are Jesus and the human race. Therefore, any human being can take part in this covenant. However, due to the provision of this covenant, it has two parts. There is one article to each of the two parts. In the first part, by belief in Jesus, every man, woman, and child can receive Jesus' righteousness, they can be saved from their sins. John 3:16 best describes this, however, the everlasting life of John 3:16 is not the super-abundant life of God described by Ephesians and other books of the New Testament. As stated before, Jesus was obligated to deal with the Jews of the four gospels as the old covenant dictated because of righteousness. After His death and resurrection a new covenant had been drafted and ratified and Jesus' title and responsibility changed. Therefore, the New Testament actually begins with Acts 1 and the four gospels record the life of Jesus, the author of the new covenant. Gaining God's righteousness is a prerequisite to gaining salvation, however, righteousness is not salvation. According to Romans 10:9 righteousness is gained by a belief of the heart but salvation is obtained by a confession of Jesus' Lordship. This confession is made verbally but through an act of obedience.
The two parts of the new covenant are drafted with two different groups of people. The first group of people don't have Jesus' righteousness, the second group does. Salvation could not be offered to lost souls but it could be offered to those clothed by Jesus' righteousness. The problem is that most all Christians ignore the article of the second part of the covenant. Without obedience, entrance is not granted. It is fine to rejoice in the gift of Jesus' righteousness, but to stop at having your sins washed away is not wise.