How Important is a Well-Known CS Degree?

syynnapse asks: "I've been interested in computer science since my mother taught me how to program in QBASIC when I was eleven, and I've wanted to be a developer ever since I learned C++ in AP Computer Science while in high-school. Now I'm in my sophomore year of college studying CS at a state university that isn't particularly known for its CS program, but I'm quite happy and personally think I'm learning plenty. My father thinks otherwise, and the deadline for transferring successfully is approaching quickly. What chance do I have in the real world with a not-so-prestigious degree? Am I likely to be learning what's important? Am I looking at a series of awful jobs if I don't transfer?"