How large does a photo have to be to get retouched?

The bigger the better.
If you think about it, the larger the file, the more pixels there are to work with, the easier it is to retouch and still keep it looking realistic.

Then again, you can really retouch anything - from 100 pixels x 100 pixels (or smaller) and up... What you can get *from* the retouching will dramatically increase as the image size increases, though.