Many depictions of the nativity have both the shepherds and the wise men at the stable on the night of Jesus' birth. However, it is commonly held that the wise men did not arrive until several months after the birth of Jesus.
What specifically is the basis for this belief?
That the wise men did not arrive until Jesus was a child and no longer an infant is derived from several Scriptures, particularly in Matthew.
Matthew chapter 2: KJV
8 And he sent them to Bethlehem, and said, Go and search diligently for the young child; and when ye have found him, bring me word again, that I may come and worship him also.
9 When they had heard the king, they departed; and, lo, the star, which they saw in the east, went before them, till it came and stood over where the young child was.
11 And when they were come into the house, they saw the young child with Mary his mother, and fell down, and worshipped him: and when they had opened their treasures, they presented unto him gifts; gold, and frankincense, and myrrh.
13 And when they were departed, behold, the angel of the Lord appeareth to Joseph in a dream, saying, Arise, and take the young child and his mother, and flee into Egypt, and be thou there until I bring thee word: for Herod will seek the young child to destroy him.
14 When he arose, he took the young child and his mother by night, and departed into Egypt:
In these Scriptures Jesus is referred to as a child and not a babe. In the following scripture is where it is thought that Jesus was at least a year old and maybe as old as two when the Wise men arrived.
Mat 2:16 KJV
Then Herod, when he saw that he was mocked of the wise men, was exceeding wroth, and sent forth, and slew all the children that were in Bethlehem, and in all the coasts thereof, from two years old and under, according to the time which he had diligently enquired of the wise men.
Even though this is not definitive it is a pretty strong argument that Jesus was no longer a babe.
If you read the account in Luke 2:1-20, you'll find no mention of Magi at the manger, just shepherds. There, Jesus is born in Bethlehem.
In Matthew 2:1-18, we find the Magi arriving at Jerusalem, from the scribes there they find out the scripture which places the Messiah in Bethlehem (2:5-6), and follow the star, which is low enough to appear over a specific dwelling, over a house, not a manger. Jesus is called a Child at that point, not a babe (1:9).
The Magi went home a different way and Herod, finding out, send soldiers to kill newborns 2 years old and younger. So Jesus was several months to a couple years older at that point.
See this wikipedia article, which mentions the Bible account in Matthew. Basically, the Bible refers to Jesus as being a "child" at the time. Also, Herod killed the male population under 2, which is probably the upper limit on Jesus' age at the time. Nothing concrete here, but enough evidence to draw a reasonable conclusion that it was some months after the birth.
Luke tells us that there was a time gap between Jesus' birth and the appearance of the Wise Men. In Luke 2:22, he says that after Mary's days of purification were completed, they took Jesus to the Temple to present Him to the Lord, as required in Leviticus 12:2-8. Purification after the birth of a male child was 40 days, so we know that the Wise Men came some time after that, since the angel ordered Joseph to flee to Egypt as soon as they left Bethlehem (Matthew 2:13).
In discussions in which I have been involved, the basis for this belief appears to be a need to harmonise the Gospels of Matthew and Luke. Luke 2:22 has the baby Jesus being taken from Bethlehem to Jerusalem for his circumcision, a little over a month after his birth, so at this stage he had not yet been taken from Bethlehem to Egypt, as we read in Matthew chapter 2. Matthew 2:16 makes it clear that Jesus was less than two years old, but how much less we do not know:
Then Herod, when he saw that he was mocked of the wise men, was exceeding wroth, and sent forth, and slew all the children that were in Bethlehem, and in all the coasts thereof, from two years old and under, according to the time which he had diligently enquired of the wise men.
Matthew certainly offers better prospects of referring to Jesus' departure from Bethlehem to Egypt being later than Luke's departure from Bethlehem to Nazareth in Galilee. It only requires that Mary and Joseph returned from Jerusalem to Bethlehem shortly after the temple visit, instead of returning home immediately, as Luke 2:39 states:
And when they had performed all things according to the law of the Lord, they returned into Galilee, to their own city Nazareth.
I would like to add a verse which clearly says that Jesus was in a house and not in the manger:
Matthew 2:11: And when they were come into the house, they saw the young child with Mary his mother, and fell down, and worshipped him: and when they had opened their treasures, they presented unto him gifts; gold, and frankincense, and myrrh. (emphasis added)
So Jesus was not in the manger when the wise men visited.
