No passport, but my birth certificate and driver's license will do just fine right?
Yes, as long as the license is a U.S. drivers license or a State - issued non - driver identification card
What would happen if I didn't have a license or state ID?
We would ask for other current not expired documents that  show your name , identifying information date of birth or age and preferably a recent photograph.  such as you employee identification card or other similar documents