You CAN get into Spain for 90 days without a tourist visa IF you are from:
Andorra, Argentina, Australia, Austria, Belgium, Brazil, Brunei, Bulgaria, Canada, Chile, Costa Rica, Croatia, Cyprus, Czech Republic, Denmark, El Salvador, Estonia, Finland, France, Germany, Greece, Guatemala, Holland, Honduras, Hong Kong and Macao (China), Hungary, Iceland, Ireland, Israel, Italy, Japan, Latvia, Liechtenstein, Lithuania, Luxembourg, Malaysia, Malta, Mexico, Monaco, New Zealand, Nicaragua, Norway, Panama, Paraguay, Poland, Portugal, Romania, Singapore, Slovakia, Slovenia, South Korea, Sweden, Switzerland, United Kingdom, United States, Uruguay, or Venezuela.
If your visa will not be ready by the time your classes start, and you are from one of the above countries, you could come to Spain and start your classes and then return to your home country to pick up your visa when it is issued. Remember, you have up to 90 days to be here without the student visa. Once you are notified that the visa is issued you have 60 days to pick it up in your home country; be careful, if you don't pick it up within 60 days, it will be canceled!
Also remember that the consulate will hold your passport while it processes your visa application, but you will need your passport to come to Spain. Therefore, you will have to ask the consulate if it will let you keep your passport while it processes your visa. The best way to convince the consulate is to bring paid plane tickets/hotel accommodations to your visa appointment. Since each consulate has a degree of administrative leeway, we cannot guarantee that it will let you hold on to your passport, but so far, all of our students and employees who have found themselves in this situation were able to keep their passports.