Hi Nick
I’m an American citizen who’s been in Spain for six years, never with a visa. Here’s what I can tell you:
1) Leaving the country to go to a non-member country only works (legally) if you leave for 90 days. I used to make this mistake, because a lot of people tell you all you have to do is step out of Spain and—voila!—you’re legal again. Not so… You have to leave for 90 days. Now, the truth is that they NEVER looked closely enough at my passport in Spain to see whether I had already been in Spain for the permitted time. But, they could. And if they do, and they see that you’ve overstayed your time, you could be put on the next plane back. So by leaving for a short trip out of the country, you may actually be putting yourself at risk of getting caught, because you have to go back through passport control.
2) If you just stay here and avoid getting into any problems with the law, you’ll probably be okay. True that in Madrid they’re starting to do random ID checks more often (coming out of the Metro, for example, especially in neighborhoods with lots of immigrants). But let’s be honest—illegal North American immigrants are not number one on their list of priorities. You can always tell them you’re here visiting a friend, and your passport is at your friend’s apartment. They’re not going to make you bother to go get it.
3) If you’re legal (i.e., in the first 90 days of your time in Spain), you can request a prorroga to extend your stay. So if you were to leave the country for a few months and then come back, you could try that approach.
Good luck!
Kronos