As far as I know, no one really hands out research electives. You can pay your way into a lot of clinical elective programs because most med schools expect you to do those as part of your basic requirements near you fourth or final year. Clinical electives are therefore openly offered throughout US hospitals and medical schools.

When it comes to research however, it's not required by anybody, and therefore you have to find them all on your own, and pay for all of your own costs. You may as well think of research electives as the same thing as "extracurriculars" on a college application. And since you're going to be doing research for someone on a very limited budget (as all research programs go), your chances of ever getting paid for a research elective are next to nil.