You will probably have both ends of the spectrum, from joe "fresh graduate from a mediocre junior college " schmoe to the “whet else can I buy” John Carmacks of the world… The important this is that you 1) Love game programming because it would be fun for you to put 16 hour days into it; and 2) Have an escape plan, if all you know about programming is games, you will be vulnerable if you need a job quick later on.
I personally have stayed away from hiring one-skill programmers. I manage business/financial-oriented programming, though, and there are lots of things to understand (algorithms, databases, platforms, web, telecommunications, etc…). Maybe game programming is more specialized and companies do not require wide knowledge. If an animator only animates, then getting a bachelor’s in two years might be worth it. Hopefully those two/three years you save do not skip over computer science fundamentals, but I cannot see how you can cover all the important stuff in such a short time without skipping really valuable stuff, like algorithms or logic (specially important for game programming).
EDIT: Another note: These days programmers that can only program are extremely replaceable, usually by much cheaper programmers from overseas. People who can understand real-world problems (ie, a verbal game concept) and translate them into computer terms (ie, requirement specs, test cases, high-level design, etc…) are the people that cannot be replaced with cheaper labor from abroad. In order ot gain these skills you must study English and systems analysis classes, not just programming classes. You must study peripheral subjects, like literartue, economics, and history. Not because you will use them directly, but because your horizons will be broadened and will help enrich the documents you write. You cannot write a business-related document if you know nothing about business (and remember that game development is a business). It does not matter how brilliant a programmer you are, remember that you also have to communicate with your boss (who may not care about programming as much as you) or with third parties.
Anyway, that’s my two cents.
