Well first I would have to point out that Spirits are different in this case to wraiths and ghosts. I only point this out because it is relevant to my point, Spirits are generally those of the higer order Valar, Maiar and so forth.
In my version of the Sil page 31 under the Headings "Of the Maiar" and "Of the Enemy" under the Chapter "Valaquenta" Account of the Valar and Maiar according to the lore of the Eldar. Just so we are very clear we are talking totally about the higher order, and now I quote.
Regarding Melkor and his followers
"For of the Maiar many were drawn to his splendour in the days of his greatness, and remained in that allegiance into his darkness; and others he corrupted afterwards into his service with lies and trecherous gifts. Dreadful among these spirits were the Valaraukar, the scourges of fire that in Middle-Earth were called Balrogs, demons of terror"
My anaylsis follows
Firstly they are referred directly to as Spirits under chapters and headings concerning directly with the higher order, they were considered Dreadful among Melkors other servants of which we know included Maiar from the text. They thusly would have to be Maiar themselves to better others. Indeed the being known as Gothmog was a Lieutenant of Melkor I do not believe Melkor would have a "lower" being as a Lieutenant.
Lastly "In Middle-Earth were called Balrogs" Tolkein was always very specific about what he wrote and how he wrote it, to me this suggests that they did not come from within Middle-Earth in the first place. The logical place they would have come from would be the same place all Valar and Maiar came from, placing them firmly in the ranks of the Maiar and the higher or "Angelic" order.