Hey Mike,
I just responded to another post of yours in a different thread. I'm in a very similar situation to you. I'm not going to Seville, though. But I will be in Madrid in about 2 weeks looking for a TEFL job. I can't offer you first-hand advice on things, but I can tell you what I've found out through research.
Getting a work visa is definitely not easy. The
Spanish Consulate's visa information site has a list of everything you'll need to do to get the various kinds of visas. The work visa is the one you need to get employment in Spain. Even if you find a place willing to offer you a visa, it will involve flying back home to the US to sign things and turn things in in person at the consulate. So that's a big hurdle right there.
Also, to hire a person from outside the EU, the employer needs to prove that you have a skill that no one else in the EU can fulfill. I've heard that one way to prove this is to advertise for 3 months. Which makes things difficult for TEFL teachers from outside the UK. Schools can hire people from the UK, which is part of the EU, without doing a ton of paperwork.
All of this being said, it seems like there are a lot of people that are working without a visa and getting along quite well. And getting certification seems to improve your chances greatly.
Hopefully this doesn't sound too morbid. It hasn't discouraged me from going. And I hope that others who have actually gone through the process will respond or point to an older thread where the issue is discussed in more detail.
Good luck and happy New Year!