I'm someone who graduated with a non-cs engineering degree (and worked professionally as an engineer) whose now in a MSCS program after trying my hand in the job market. Not for a lack of trying, but my experiences definitely relate to an uphill struggle just to get even noticed. And before anyone says "you should do x|y|z", I've done my part pretty well. A few decent sized personal projects, constant studying, meetu…
I haven't had a hard time finding something since then. I do hate the basic algorithms questions every interviewer asks, but a month or so of Coursera and I'm ready to answer all of the "Implement a QuickSort algorithm in 20 minutes" questions again.
You either need luck or you need to be willing to take a job that isn't as reputable to learn programming as a profession, once you have that many doors will open up to you.