If you don't have a taxpayer number and write "exempt", you will not be able to e-file, and you will have to print and mail your return in. That may add 2-3 weeks to your refund processing time, but does not affect the amount of the credit. Also, if they pay employees, they must have an EIN, even though they don't pay income tax. So there's no reason for them not to give it to their clients.
