If you enter any random number as Turbo Tax suggests, this will seriously delay the processing of your STATE taxes, and possibly your federal, as they do look to confirm EIN's to verify each employee is reporting what each employer has reported as being paid to them.
Many states have free databases to lookup the state EIN's for businesses, begin with your local county websites, and work your way up to the state website searching for these tools. I've found that many states offer these for free, it just takes a bit of time to locate. Good luck!
