I think that Eli eli lama sabachthani is undoubtedly an intentional reference to Psalm 22:1. The question of why, in His extremity, He might have done it, is something else again.
First, He was “steeped in the Scriptures” – He knew the Tanakh very well indeed. It’s evident in His teachings that He always has the apposite quote from it, and will often deflect baiting about one passage by citing an entirely different one.
Second, there’s a very famous literary passage, the details of which I don’t recall, about some Jewish soldiers who died “with the Sh’ma on their lips.” Christians of all sorts pray the “Our Father,” Catholics and Orthodox the “Hail Mary,” T.H. White in a moving passage has Merlin see Arthur “get it” at the end of his childhood training and then Merlin says the Nunc Dimittis." And some people are suggesting that “The Star-Spangled Banner” be replaced as national anthem by “My Country 'Tis of Thee.”
What these incidents have in common is that the affirmation, prayers, canticle, and patriotic anthem in question are referenced by their opening words. As of course is Psalm 22.
It is possible that in His extremity Jesus, whom it is important to remember is in orthodox understanding truly God and truly man, participating fully in our human nature, experienced the last missing element of this: the loss of faith and despair. And that Eli eli is a cry of despair.
But even more plausible, considering that He is “tempted in every way as we are, yet without sin,” in Paul’s language, is that He experienced that sense of losing faith and despairing – and conquered it.
It’s instructive to read Psalm 22, because it starts out with that soul-wrenching cry of despair. And continues as a spiritual exercise ending in a quiet heart again calm and firm in faith.
Jesus loved to teach by example, and this may have been His last bit of doing that. “Here’s what you do when you’re being martyred and tempted to renounce your faith and give up on God. Watch Me do it!”
Gigi, I’m absolutely certain that Jesus knowingly acted out some elements of Messianic expectations, even as He rejected other ones because they didn’t fit what He came to do. But I’ve found that “playing the fulfillment of prophecy card” is something best done in homeopathic doses. After all, we’ve all witnessed, right here on this board, an avenging angel cast out Satan for encouraging flames, and Eve reveal that she was in sober truth made from male body parts, just as a fundamentalist reading of Gen. 2:21 would explain. And I might point out that richness in poverty and remaining staunch for the truth of patience and love while the noisies claim to be doing God’s work while actually spreading hatred, are pretty fair descriptions of what I’m supposed to be doing here (not that I don’t often let my angry and polemic side show lately :(). Now, remembering that “angel” means “messenger, spokesman” as well as “supernatural being,” and was used in apocalyptic to reference the bishops (and elders) leading the local churches, read Rev. 2:8-11.
Anyway, where I’m going with that is that you can easily overdo the “fulfillment of prophecy” idea. Jesus did what He did because they were necessary and important steps to carry out His purpose. If at times He made sure that they were acting out an Old Testament reference as well…