Here's why it's unlikely to have a specific origin:
* No dictionary entries: No standard dictionaries or etymology resources list "whole shiteree."
* Lack of common usage: It's not a phrase that is commonly used in everyday language, literature, or popular culture.
* Possible mishearing or misspelling: It could be a mishearing or misspelling of another phrase, possibly "whole shebang" or a similar expression.
If you heard this phrase used, it's likely a joke or a play on words.
If you have more context about where you heard it, it might be possible to determine the origin. For example, was it used in a specific region or community? Was it used by a particular person or group?