If you look at my signature, you'll see it mentions a book I wrote. Shortly after I wrote it, an Amazon.com recruiter approached me at the Open Source Convention where I was promoting the book. Sadly, he wasn't able to offer me a job because I didn't have a degree.
Based on the last eight years of professional experience, I'll tell you that you already have a leg up on where I was when I started, simply by having the degree. I agree with VIPStephan here - the degree helps a little, but the experience really matters.
I would suggest finding an open source project that interests you and getting your experience by helping them out. That's really how my career started. Also, don't be afraid to get your hands dirty in code.