Didn't really read the other replies, but here's what I can say:
I work as an ED tech in a busy department in or around Boston. I have worked here full time since 2006, when it was easier to get a job than it is now.
My department (and affiliated hospitals) require either an EMT, CNA, or 2+ years tech experience. You can mix and match. CNA is preferred over EMT.
I got my EMT-B cert, applied, interviewed, and got the job. The hospital then sent me to a variety of classes: EKG, phlebotomy, an ortho class (for fiberglass splints, cast removal, ring cutter, crutches/canes, air casts, Bledsoe boots, post-op shoes, etc), orientation to sterile fields (for assisting in ED procedures, Foleys, etc), psychiatric non-violent intervention, restraints, and basic self-defense, and some other garbage.
I say to try and get experience with your EMT, or at least volunteer in the ED and get to know people. They definitely prefer to hire people with good references from WITHIN the hospital. If you can get phlebotomy experience (but not necessarily take a course), it might help. Or any experience in any of the technical stuff you will do as an ED tech.
You will work hard, and make less than pretty much EVERYONE else in the department. My secretary girlfriend makes a lot more than I do. But I do make more than I was offered by local EMT services.