That's a tough one.

I agree that honesty is best here.

My thought on this is that maybe you could first explain how much you love her, how much you want to be there for the wedding. How excited, etc.
Then tell her that you just can't afford it right now, due to your financial state.
Maybe you could ask her to pay for all or part/half of the expense? That way you could afford it/not have to "afford it" and this girl could still have her dream wedding. If as you say they are well off, and this means so much to her it would make sense.

I have a friend who doesn't understand money either. I don't really know what to do with her sometimes. Try your best - wishing you the best of luck.