I know that people who worked hard for their Engineering degrees will naturally be suspicious of anyone who seems to have done less work than them, but even so I was rather amazed at the amount of ignorance and hatred in the responses here. As a Literature major who now makes six figures programming, please do ignore them.
My advice would be to enroll at Hack Reactor or a similar coding boot camp. We've hired two programmers from them: one was a Biology PhD, the other just had a Chinese Literature undergraduate degree. In both cases we didn't really care what their degree was, we cared about their abilities. Based on what I've seen, the best of the graduates of Hack Reactor are WAY better hires than an average CS graduate (and they're a lot easier to hire; the Googles of the world snatch up the top CS graduates before smaller companies like ours even have a chance).
Of course, I personally didn't take the boot camp approach. I graduated, spent a year unemployed, then managed to get a position as a web designer for a small company. It was a terrible company: they wouldn't even pay for water for employees! But as annoying as their cheapness was, it was that very cheapness that got me hired. Because I was willing to work for $15/hour and could do the work (I'd taught myself web development) I was able to get that crucial first job. You may have to hold your nose in a similar way to get your first job, if you don't take the boot camp approach.
Once I got my foot in the door by working their a year I moved on to a junior programming job, worked my way up to being a team lead, and then moved on to my current company (a start-up). I'd imagine you could do something similar, but going through a boot camp will give you that "foot in the door", which is really the hardest part for someone in your position. After the boot camp gets you your first job, that job will get you all your future jobs.
So, ignore the negativity here. Silicon Valley really is, at least to a large extent, a meritocracy: what matters is being good at your craft, not where you came from.