America is NOT a melting pot.  Never has been and never will be.  This is secular humanist propaganda.  
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What united Americans was a common Judeo-Christian heritage and a common language.  As America has moved away from that heritage we have fragmented as a people.  We are now black, white, male female, Christian, atheist, straight, gay, rich, poor, entitled, independent, pro-life, pro-choice, liberal, conservative and so on.  
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If you go to New York City you will find enclaves of blacks, whites, Jews, Italians, Chinese, Puerto Ricans, Muslims, etc.  These groups coexist.  They have not melted and become one in any material sense.
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Unity is of the Spirit .  The Spirit is the ONLY thing that truly unites.  What is the spirit of America today?  It depends on who you are talking to.  
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We have a responsibility to obey the great commission.  
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Matthew 28<br><i>
18 And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth. 19 Go ye therefore, and teach all nations, baptizing them in the name of the Father , and of the Son , and of the Holy Ghost : 20 teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, even unto the end of the world. Amen.</i>
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When Americans come under the authority of Christ , His Spirit will unify us. 
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Nothing else will.