<p>I am building up a view with various text and image elements.</p>

<p>I want to display some text in the view with a blurry copy of the text behind it, but not just a text shadow.</p>

<p>How do I apply Gaussian blurred text onto a UIImage or layer?</p>

On the desktop, no question, you'd use CoreImage to do this.
On the phone though, I don't think there exists a way to do this using CoreGraphics. If it is absolutely critical OpenGLES may be able to help.
However, I would suggest rethinking your interface. I would think the blurred text would be distracting.
Edit: mledford points out in the comments that you could use CoreAnimation. I don't know if CA on the phone includes blur radius like on the desktop, but you could try it.