Knowing that part of the inspiration for the song was from reading about Elvis and Priscilla and their relationship, and how she looked up to him ...
I think the song speaks to the idea that each person is looking for a personal "Jesus" in the sense that they are looking for almost a ... formula ... to be fulfilled in their life, and they want this done by another person. It may not be conscious, it may be an unconscious drive or motivation they aren't even aware of.
Perhaps they want to find a person who restores hope in mankind for them, or hope in themselves. Perhaps they want to find someone who can "prove them wrong" about their view of people. Perhaps they need someone they can hurt and harm, and that someone won't abandon them in the process. They'll survive, and even love them despite it. Someone they can crucify, so to speak. Sacrifice.
I knew a girl who needed this in her own life, for example. She came from a horrific family ... her father was a murderer, killed his own sibling. Yet, he also sought to protect his daughter at all costs, so long as she recognized his authority. She had a mixed view of him: a monster and hero, all rolled into one. When she finally fell in love in life ... the person she fell in love with, she wanted this person to *suffer*. She respected the guy, he was the first person she fell in love with like that, opened up too ... yet she needed to know that he could suffer, and withstand her emotional blows and pent up fears and anger. So she eventually could only feel loved, if they were apart. It gave meaning to her life, to know that he was hurting and in pain, for HER. Arguably, she wanted to take her anger and fear out on her father, and family that tolerated them. But deep down, she viewed them as weak and ignorant. Taking out all the twisted knots in her life onto them wouldn't accomplish anything, because they were "guilty" in her eyes, and she knew better. In her eyes, it was loving to tolerate them because they were weaker. So instead of unleashing that darkness on the guilty ... she wanted to do it on someone she trusted and loved. Someone whom it would actually matter to her, and they them. Someone who in the end, would understand why she did it all, and let her hurt them. Someone for whom it counted. So in some ways, she sought someone to sacrifice to give her peace. I very much saw her as essentially needing her "own personal Jesus." Someone whom she could harm, and take out her need for justice, her fears and anger ... yet whom she trusted and loved nonetheless. A very specific role for her, sort of balancing out a formula in her life that was there. She didn't even know it was there until she met him and loved him, and it became apparent. She found peace, by "crucifying" the one she loved. Her own personal Jesus.
That example is a bit complex, as the average person may not need their own "Jesus" for the same reasons. But I think it's probably more common than we realize, the need and desire to find another person who fulfills a need in our life but in a way that involves things typically ascribed to Jesus ... not just our desire to be accepted, at home with another person, loved, but sometimes our need to find emotional and mental justice, someone to redeem life for us and give it meaning, someone to mentor us and show us truths and surprise us in ways we couldn't have predicted, etc.
