1) If marriage is a religious institution defined by biblical principles then the government has no authority to establish marriage as the only legally recognized civil union. (Congress shall make no law respecting an establishment of religion (1st Amendment)).
2) If the government is going to define marriage and thus the benefits thereof, then it cannot restrict those privileges to certain citizens (No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States (14th Amendment)).
So, the government is bound by the constitution to either:
1) Legally recognize the civil union of any two consenting adults and relegate marriage to a religious institution.
2) Lift the restrictions on marriage.