If you are serious about getting a programming job then you should make sure you get a degree from an institution that is respected by companies looking for coders. It certainly wouldn't be a course in C++ from your local community college, you'd want at least a bachelors in computer science from a reasonably respected university. Computer science is much more than just learning C++, you need to understand design patterns/algorithms/etc., and you'd also want other areas of expertise such as math, DSP or physics as that's what you might be applying with your coding.
In the places that I have worked (video game industry) that's pretty much the bare minimum, and even with that it can be hard to get in, only the best graduates would be picked that showed us something special. We'd also often typically only hire students that have done a co-op (work practicum) with us that have proven to us that they know what they are doing.
You don't necessarily need this super fancy degree stuff to get hired if you can show a lot of entrepreneurial qualities and experience (e.g. you taught yourself or did just take that community college course and started your own company that actually produces products or similar). However you'll have to be pretty good at that and demonstrate that you can work with or manage others. That's one of the points of university, it's more than just coding, it's seeing if you have what it takes to get through all of it, you have to be reasonably well rounded to manage that - coding isn't everything.
Myself I only went to a 2 year technical college, but I got a bit lucky due to specializing in something rare at the time that was in demand. If I looked at the employee makeup of places I work I'd bet at least 90% have a bachelors from university, and a lot of people even went for a masters. The other 10% either got in a long time ago or have just proven to be damned good at what they do. It all probably depends into what line of work you get into though, it's demanding in mine, maybe not so much in some others.
