I work at a Level I center in a medium-sized midwestern city, and it's one with an EM program that is respected and sometimes bragged about. Most of my fellow techs are CNAs; there are some medical assistants, a gaggle of EMT's like myself, and even a few Paramedics around.
I got the gig because I was an unpaid volunteer for about 8 or 9 months, so they knew I was ignorant but not dumb. When I earned EMT last fall, they asked me, "so, when are you going to apply?"
I recommend this method because it allows you to scope out the working conditions and the people, and it allows them to check you out as well. Plus you can be a volunteer (clean rooms, make beds, run stuff to the lab, do not touch the patients) while you're still doing whatever training you plan to do.
See also the thread "Respect for the Techs" for some notes from various ED people about how to be a kick-ass tech and make life easier for yourself and your colleagues.