My major was in Brain and Cognitive Sciences and I've been working as a programmer in NYC since I graduated (May 2013). I took a few programming courses in college but don't have a formal academic CS credential.
My experience has been that once you get your foot in the door, your degree doesn't matter. I got my first job on Craigslist. It was a shitty work environment and paid 45k (which in NYC ain't much), but I needed experience (and proof of income to move out of my mother's one bedroom, ha). Fast forward to today, I've just received an offer from a fast growing startup for 120k. Compared to what the best folks in NYC are making it's not that high, but not bad considering where I started.
My advice is that while things will be a bit harder in the beginning, staying hungry and ambitious and doing your best to constantly learn will have you quickly outpacing those who don't have the same level of drive. My policy at the jobs I've held has been to volunteer for every single task that I can. I don't even think about it anymore; if there is something that needs doing late at night or on a weekend, I just say yes. I probably don't need to do this as much anymore, but I think it helped me seem more useful when I started, especially since in the beginning there were pretty big gaps in my CS knowledge. Between that and reading Hacker News obsessively I've become the go-to guy for many projects (seriously, I attribute a significant amount of my career success to reading about new technologies on HN).
Also, for what it's worth, I don't have any kind of public portfolio and I've never had anyone ask for one. I'm sure it couldn't hurt though.
Good luck!