I don't think you are nuts, but be realistic in your expectations for your first job in the industry. There will be plenty of competition out there that could have a lot more experience - you just need to focus on showing why you are passionate about starting in this field and that you are not only capable but also willing to learn anything required to improve your potential within their companies.

If I saw this kind of drive I would (and have in the past) overlooked people's actual experience. Someone with a go-to attitude and very eager to increase their skills will always do well in an interview with me.

Good luck and don't let the current job market bring you down - it'll happen sooner than later.