For my IL tax refund, turbo tax says I need to enter Spein, but I have no clue what that is and searching in turbo tax was not helpful.

Can you give us the context in which this word is used? 

It shows up during "Fix Errors".   Below is what the page displays:

Check This Entry

Schedule IL-WIT Income Tax Withheld: Spein must be entered.

Spein:   <enter value>

All, this refers to the "Federal ID" of the payer on your W-2.  If you received unemployment benefits it will be the "IDES Federal ID" on your 1099-G form.

Could that be the "SPouse's"  EIN on their W-2 form in the state section box 15 ?