Blood of the New Covenant offered to whom? In Luke 22:20 Jesus says that the blood of the new covenant is poured out for "you". Is the word "you" only referring to the apostles only? Or is it meant to represent all of humanity.
The 11th century Byzantine commentator, Theophylact of Ohrid, who wrote a comprehensive commentary on the Gospels compiled from the writings of earlier Church Fathers, wrote:


  When the Lord says, which is given for you and which is shed for
  you, He does not mean that His Body was given and His Blood was shed
  only for the Apostles, but for human nature itself.  Therefore,
  whenever He says, Given for you, understand it to mean, "Given for
  the human nature which belongs to you all." (An Explanation of the
  Gospel According to St. Luke)


I think that one could say that this interpretation is also reflected in Matthew's and Mark's accounts, where they recall Jesus saying which is shed for many:


  Matthew 26:28
  
  
    For this is my blood of the new testament, which is shed for
    many for the remission of sins
  
  
  Mark 14:24
  
  
    And he said unto them, This is my blood of the new testament, which
    is shed for many