Just my own little anecdote, but I was able to get into upper middle class after 4 years and no degree. I've never completely passed an algorithms interview either - most of my jobs haven't had algorithm filters. I'm now doing functional programming in a cool language for a living.

Most people I meet haven't had my path to success, but it is possible. My gut feeling is that I'm a small statistic because people give up quite easily when they think their goals are unattainable. My first programming position took me 15 interviews to land a job!