I agree with LarryC's advice. You committed to teaching the classes when you were hired, presumably, and you've tried to tell them that you're not a Ph.D.
That said, I'm in a dis/similar position to yours -- I'm a visiting instructor (starting in two weeks! yea!) who told the search committee I'd have my Ph.D. soon, and now it's looking like months and months. I've hinted to them that I won't become a VAP as quickly as anticipated, but I'm scared to tell them outright about the disagreement with my advisor that's lead to major dissertation overhauling.
wannabeprof: it may not matter a bit. I was in a similar situation, and my department didn't care about my Ph.D. since they regularly hire ABDs to teach the courses I would be teaching. When I finally did finish my degree, I got a letter from the Dean saying "Congratulations on your degree. You have been promoted to the rank of Assistant Professor of English." The following day I got a second letter. It read: "We congratulate you again on your degree, but please disregard the previous letter. You have been promoted to the rank of
Visiting Assistant Professor."
treehugger1: One small piece of advice no matter what you decide. Presumably, someone at this school will be writing you a letter of reference if you're looking for a TT position. Be absolutely certain that whoever writes that letter gets the title correct in their letter; you really don't want to have to explain why your reference thinks you're a Visiting Assistant Prof when you only claimed to be a Visiting Instructor.