Did Jesus leave his throne when he became Man?

Christmas carols often claim that the Son of God "left his throne" when he became man. A few examples,

There was no room in Bethlehem

for Him who left his throne

Thou didst leave Thy throne

and kingly crown

The Lord of hosts, the God most high,

who quits His throne on earth to live

The trouble is that I'm at a loss as to what all that is supposed to mean. When he became man, did the Son abdicate his role in the lordship of the Trinity, ceasing to rule the cosmos together with the Father and the Holy Spirit? What does such a construction do to our doctrine of the Trinity? Besides, Scripture bears witness to the fact that the Son was involved in upholding and guiding the universe before and after he was made flesh, Colossians 1:15-17, Hebrews 1:3. And Hebrews 1:8, citing Psalm 45:6-7 insists that the Son's throne is "for ever and ever". 

The nearest Scripture gets to the idea that Christ "left his throne" is in using spatial language to describe the incarnation. In the Gospel According to John Jesus often testifies that he came down from heaven to earth, John 3:13, 6:51. But even here, we need to understand that this language is figurative, accommodated to our capacity as creatures constrained by space and time. Being of the same divine essence as the Father, the Son is omnipresent. He was not shorn of his immensity when he became Man. In the words of Augustine, Jesus  became was he was not - fully human, without ceasing to be what he was - fully God. The one who was born in Bethelem  was at one and the same time filling heaven and earth, unconstrained by the restrictions of created space. When Scripture speaks in terms of the Jesus coming down from heaven, this language is intended to convey the dazzling height from which he stooped when the Word was made flesh. 

But still, even as he was born of woman, born under the law, Jesus was the sovereign Son, ruling over all things together with the Father and the Holy Spirit. Rather than depicting Christ as surrendering a throne at the incarnation, the bible insists that he came to claim his crown as the Redeemer-King of the people of God, Isaiah 9:6-7, Luke 1:31-33. The incarnation was not an act of dethronement for the Son, but of further enthronement. Because he who was the form of God took the form of a servant and became obedient to the death of the cross, God exalted him to his right hand in glory.  Jesus is the Lamb in the midst of the throne, worthy to reign because he redeemed us to God by his blood, Acts 2:36, Philippians 2:8-11, Revelation 5:5-6, 9-10. 


Well might angels sing in wonder
as they herald forth his birth;
even they can scarcely ponder 
why God's Son came down to earth.
See Him now, enthroned in glory,
earth awaiting His return.
While our hearts recount the story
may these hearts within us burn.
(Graham Stuart Harrison)