First off, most private schools ask for a degree along with the TEFL certificate. However, you may be lucky and get something if you happen to be in the right place at the right time. The difficulty is that most jobs are in the big cities but there they tend to ask for better qualifications. If you are in a small town then there are perhaps just one or two schools there and if they don't have vacancies then you have to move to another town to work (and/or live). In the big cities there are more schools but, as I said, they often ask for a degree.

Also you don't mention where you are from. If you're from outside the EU then it will be extremely difficult to get work due to visa issues.

Finally, although you probably knew this, Spain is in mid-recession and jobs are harder to come by. If you are there in person then you might stand a chance but make sure you take enough extra money to be able to survive for a few months without work and leave when you run out.