I am planning to leave for sevilla in a few weeks/months. At first, I intend to take a few classes at CLic, and while doing that hope to get some kind of job/internship. I have a BA in Spanish, some internship experience in Madrid, and two years of work experience here in the U.S. I am wondering if I should even think about a visa- I don't want to cheat the system, but also don't want to rule out my chances of making money. Does anyone have any suggestions/advice?

Why not try applying to TEFL (teaching English as a foreign language). I know they have offices in Madrid, but don't have a contact number for them. I am sure they could help in your search for employment.
Good Luck.