From my experience, the largest hurdle first time programmers have is being able to execute programs in their head. It takes a cognitive leap to go from the source code in front of them, and what happens at runtime.
I believe that if you have made that cognitive leap, you can call yourself a programmer. It means you’ve entered into the second hump – you are a programmer. One of us. Welcome :)
This is also the reason why solving programming challenges at places like InterviewStreet Challenges, CodeChef, TopCoder, SPOJ, etc also increase your general programming skills – they require that you continuously run code in the interpreter in your head. Helps you train your procedural memory. Same reason why learning different language paradigms (OOP, Purely Functional, Procedural, etc) makes you a better programmer.
Reminds me that I have four more chapters in SICP to finish and Clojure to learn :)