I also agree with Escalla. It's a lot easier to start off volunteering/shadowing somewhere and let them see that you're eager, hard-working, responsible, etc., and then when a job opens up, they'll think of you. You can get a job in an unrelated field, or even somewhere animal-related other than a vet clinic, in the meantime if money is an issue. The job market is tough for both vet assistants/techs and vets, but that's because the field is becoming oversaturated, not a reflection on you as a person.
If your parents do feel like you're wasting their money, it might help to point out that the real waste would be applying when you know you don't have the experience to have a chance to get in anywhere, and would be sacrificing focus on your senior year grades (assuming that is how you feel, maybe I'm reading too much into your post). If they would be the ones paying for your application fees, GRE, traveling to interviews, etc., those costs add up quickly.
I applied last year when my grades and experience hours really weren't up to par, and I'm now taking a gap year by default rather than by choice, and applying again with a much more competitive app (although my stats still aren't great). On one hand I'm glad I applied last year because now I know how the whole process works (and I found SDN!
), but from an objective standpoint it probably was a waste of my parents' money. They also supported me a lot though undergrad, but when I found out I wasn't going to vet school this year we were able to come to an arrangement where I'm now mostly financially independent. I don't know if that would be possible for you, but it's something to suggest to your parents that might make the news easier to take. Plus you've got a year to save up money, since you're not finding out in April that you'll be taking a gap year like I did!