Biblical citations in the hymnal: Luke 2:7; Mark 10:14-16; Matthew 1:23, 28:20
Luke 2:7: "And she gave birth to her firstborn son and wrapped him in swaddling cloths and laid him in a manger, because there was no place for them in the inn."
Mark 10:14-16: "But when Jesus saw it [His disciples' rebuking the crowd's bringing children to Him], he was indignant and said to them, 'Let the children come to me; do not hinder them, for to such belongs the kingdom of God. Truly, I say to you, whoever does not receive the kingdom of God like a child shall not enter it.' And he took them in his arms and blessed them, laying his hands on them."
Matthew 1:23: "'Behold, the virgin shall conceive and bear a son, and they shall call his name Immanuel' (which means, God with us)."
Matthew 28:20: "'... teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age.'"
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The text is public domain:
Away in a manger, no crib for a bed,
The little Lord Jesus laid down His sweet head.
The stars in the [bright] sky looked down where He lay,
The little Lord Jesus asleep on the hay.
The cattle are lowing, the baby awakes,
But little Lord Jesus, no crying He makes.
I love Thee, Lord Jesus! Look down from the sky,
And stay by my cradle till morning is night.
Be near me, Lord Jesus; I ask Thee to stay
Close by me forever and love me, I pray.
Bless all the dear children in Thy tender care,
And take us to heaven to live with Thee there.
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The verse from Luke shows up in the descriptions of the setting in the first two verses of the hymn. "In a manger" is the only specific description taken; it seems that "on the hay" and the presence of "the cattle" are extrapolations.
Jesus' being with us is the common thread in the two verses cited from Matthew, and this appears in the second and third verses of the hymn. In the second, there's "stay by my cradle," and in the third, "Be near me, Lord Jesus; I ask Thee to stay / Close by me forever...."
Jesus' blessing the children in the text from Mark is in the third verse of the hymn, specifically: "Bless all the dear children in Thy tender care." His saying "for to such belongs the kingdom of God" and "whoever does not receive the kingdom of God like a child shall not enter it" might have some bearing on the hymn's "take us to heaven."