Is more desire than experience marketable?

I've read in several places online that companies would rather hire an inexperienced programmer over an experienced one because they are more "teachable". Starting with a "fresh" programmer gives the company an opportunity to train them the way they want.

However, searching jobs online I don't see this at all. Most jobs I find require at least 2-3 years of experience and are looking for people that really know what they are doing.

I have such a strong passion and desire to become a programmer. I've been so thirsty for knowledge that I'm taking every extra minute I get to learn a bit more. I can't stop thinking about programming and think of it so much that I'm even programming in my sleep. However, I'm currently in a completely different field. I'm dying to jump ship and get started with my programming career but by the looks of things it's at least a year or two out.

I haven't created anything worth showing off, obviously because I'm just starting. Are there really companies out there that would be interested in someone that has more desire than experience or do I just need to put the job search on hold until I have something to show for (do some freelance work and build up my portfolio)?