This game is a knock-off of the ancient television show "Name That Tune."  Divide into two teams.  The leader has a list of well-known Bible verses each with about 10 or 12 words.
 
The Play
The two teams each send one person to compete in the first round.  A player "bids" on the first verse.  For instance, "I can name that verse in six words."  The other player then can say, "I can name that verse in five words."  The bidding continues until one player stops bidding. (A player would stop when he/she thinks the opposing player will be unable to complete the verse with so few words.)
Whoever wins the bidding gets first chance at winning the point. The Leader reads only the number of words bid. If the first player doesn't answer correctly, one word is added and the second player gets a chance to complete the verse. If the second player doesn't complete the verse correctly, then it goes back to the first player again with an additional word, and so on.

Example of Play 
The players start bidding at 8 words. When Player B bids "3 words," Player A drops out. The Leader reads the first three words of the verse, and Player B must finish the verse correctly.  If Player B is successful, team B gets a point.  If unsuccessful, Player A gets an additional word (ie. in this case 4 words) and the opportunity to complete the verse.  If successful, team A gets the point.

Variations
If the players keep bidding low, but needing more words to get the answer, make the game more risky by giving two points if the bid winner misses the answer but the opposing player gets it right.  It is even riskier if the second player is allowed to consult team members before answering. Another variation would be to give bonus points if the player can also name chapter and verse.
 

Some Bible verses you can use are:
  John 3:16 For God so loved the world ...
  Genesis 1 In the beginning God created ...
  John 1 In the beginning was the Word ...
  Luke 2 In those days a decree went out from Caesar Augustus ...
  Luke 2:14 Glory to God in the highest and on earth peace ...
  Luke 2:16 And they went with haste, and found Mary and Joseph ...
  Matt 5  Blessed are the poor in spirit ... (and other Beatitudes)
  Psalm 100 Make a joyful noise to the Lord ...
  Psalm 23 The Lord is my shepherd, I shall not want ...
  Mark 15:34 My God, My God, why hast thou forsaken me?
  Matt 28:19 Go therefore and make disciples of all nations ...
  Gen 1:22 And the rib which the Lord God had taken from the man ...