Lambda the Ultimate

In Turner's paper "Total Functional Programming", as seen on LtU here, on page 16 it says that in a total functional language it's impossible to write an interpreter for that language. I've seen this statement in other papers too. None of them I've seen have shown or made reference to a proof. Some mumble about the halting problem. Can anyone provide a link to a paper with a proof of this, or sketch a proof themselves?

It seems to me that if one were to have a language that required the programmer to give correct termination proofs of all functions, then if one could prove the termination of an interpreter for that language, one could write the interpreter in that language. That must mean that one couldn't prove the termination of an interpreter for a total functional language. I'm curious to know why.