Advice for TESL/TEFL Employment & Work Visas

I'm new to this forum and I'm in desperate need of some advice and insight. I recently obtained my TESL/TEFL certification and I'm looking to move to Spain (preferably Madrid) to begin teaching English as soon as possible. The company through which I obtained my certification has had me under the impression that English teachers are in high demand in Spain and that hiring occurs year round. However, I have only heard from one potential employer whose position openings do not begin until September/October. Might anyone have any advice for finding a position teaching English that hires over the summer? I am an American, not an EU citizen and I do not have a visa. The company that I received my TESL/TEFL certification from initially had me believe that employers would sponsor a work visa for me relatively easily, but this has not proven to be the way it works. Please, any advice helps! I am simply ready to begin working and moving AS SOON AS POSSIBLE and I'm just looking for a reputable employer who will sponsor a work visa for me. Thanks!