Abram Meets Melchizedek Figure of Eternal Priesthood

In Genesis 13 Lot and Abram decide to go their separate ways and Lot settles in the Jordan plain and Abram to Canaan which the Lord gives to Abram. Genesis 13:14-16 [14 The LORD said to Abram after Lot had parted from him, "Lift up your eyes from where you are and look north and south, east and west. 15 All the land that you see I will give to you and your offspring forever. 16 I will make your offspring like the dust of the earth, so that if anyone could count the dust, then your offspring could be counted. ]
After this in chapter 14 we find Abram saving Lot who has been carried off by a coalition of four kings who had attacked a combined force of five kings. The kings of Sodom and Gomorrah fled and their cities were looted and Lot and his possessions were also seized because he was living in Sodom.
Abram comes to Lot's rescue with a force of 381 trained men. The small size of this force puts the whole account into some perspective.
In Genesis 14:18-20 we find the mysterious figure of Melchizedek
[ Then Melchizedek king of Salem [i.e. Jerusalem] brought out bread and wine. He was priest of God Most High, 19 and he blessed Abram, saying,
"Blessed be Abram by God Most High,
Creator of heaven and earth.

20 And blessed be God Most High,
who delivered your enemies into your hand."
Then Abram gave him a tenth of everything.]

There are only ten references to Melchizedek in the bible. This one, one in Psalm 110:4, and the eight references in the epistle to the Hebrews.

Psalm 110 of David

1 The LORD says to my Lord:
"Sit at my right hand
until I make your enemies
a footstool for your feet."

2 The LORD will extend your mighty scepter from Zion;
you will rule in the midst of your enemies.

3 Your troops will be willing
on your day of battle.
Arrayed in holy majesty,
from the womb of the dawn
you will receive the dew of your youth.

4 The LORD has sworn
and will not change his mind:
"You are a priest forever,
in the order of Melchizedek."

5 The Lord is at your right hand;
he will crush kings on the day of his wrath.

6 He will judge the nations, heaping up the dead
and crushing the rulers of the whole earth.

7 He will drink from a brook beside the way ;
therefore he will lift up his head.

The figure of Melchizedek appears to be eschatological since his name is associated with eternity. The epistle to the Hebrews will associate this mysterious figure with Christ and the sacrifice of bread and wine offered in Jerusalem by Melchizedek becomes a prefigurement of the Eucharist and Christ the eternal high priest.

The Infancy Narratives

As I mentioned there is much ado about nothing in the scholarly treatment of the infancy narratives because of the fact that the two evangelists, Matthew and Luke handle the story so differently. However there are no real conflicts in the two stories especially when you realize that that stay at Bethlehem could easily have extended over a period as long as two years prior to the flight into Egypt.

In reading the two treatments a direct harmonization can be accomplished in the following fashion:
Lk 1:26-38 The Account of the Annunciation and Mary is told that Elizabeth is pregnant.
Lk 1:39-56 Mary Visits Elizabeth staying about 3 months (Mary 3+ months pregnant)
Mt 1:18-25 The Birth of Jesus Christ (Matthew's account up to Joseph accepting Mary into his house)
Lk2:1-7 Journey from Nazareth to Bethlehem for the census and the birth of Jesus

Note that here we have the first apparent conflict between the two accounts. Luke begins in Nazareth and sends Mary to Elizabeth back to Nazareth thence to Bethlehem for the census. Matthew by contrast seems to begin in Bethlehem and stay there. He is actually silent about their location until after the birth of the child.

Lk 2:8- 20 The Shepherds and the Angels (Matthew is silent about this)
Lk 2:21-38 Jesus Presented in the Temple (Birth + 8 Days) (Matthew is silent about this and the prophecies of Simeon and Anna)
Mt 2:1-12 The Visit of the Magi (Birth +|- up to two years probably a year)

To reconcile the two accounts one only has to assume that Joseph and Mary stayed on in Bethlehem which is near Jerusalem for a year or so while the child was small. This is certainly reasonable since one does not like to make long journeys with an infant if one doesn't have to, especially on foot. Since Herod ordered male children up to 2 years of age killed it is clear some time had passed since the Magi had seen the star and Herod was uncertain of the child's age.

Mt 2:13-18 The Escape to Egypt (Joseph in accord with an angelic visitation in a dream flees with Mary and the child to Egypt) by now the child is between one and two and likely can walk.
Mt 2:19-21 The Return to Nazareth ( Circa 4 BC when Herod Died) and finally we can conclude with the passage from Luke:

Lk 2:39 39When Joseph and Mary had done everything required by the Law of the Lord, they returned to Galilee to their own town of Nazareth. 40And the child grew and became strong; he was filled with wisdom, and the grace of God was upon him.

It is reasonable to ask where the difficulty is? There are several usually cited. One is the dating of Quirinius as governor of Syria when this first census took place. I won't bother with that, but Quirinius was in the area in the proper time frame and it is not difficult to harmonize all the dates. The only other questions involve the silence in Luke about the Magi, Herod's attack and the flight into Egypt. Some of these fit Matthew's plan and ideas about what is significant more than Luke's. Luke is writing to Gentiles who don't care much about Jewish customs and ways while Matthew is writing earlier and trying to link Jesus to prophecy. He may know about their original home in Nazareth and yet also know they had lived a significant time in Bethlehem and the Messiah must be born in Bethlehem of Judea. It may be as simple as that.

So there are not very many problems. I heartily recommend the book The Mother of Jesus in the New Testament by John McHugh for those who seek more reading on the general subject.