I agree wholeheartedly with what Lisa wrote above. First off, kudos to you for asking this question--it's a really important one. When I decided to get my creative writing MFA, I didn't think much about jobs. All I knew is that I wanted to write, and I figured the rest would sort itself out. It hasn't been quite that simple. For a long time I took a bunch of random jobs--waitress/bartender, researcher, paralegal--but after a couple years, I started figuring out how to use my writing skills for work. While an MFA might not be the most impressive degree on a resume, the ability to write well is a huge asset anywhere, and is something you want to play up as much as possible. I was able to use my writing ability (which you should mention and demonstrate in any/every cover letter you write) to help me land jobs in editing, marketing, and consulting. I wrote and edited copy for a physicist's website, wrote professional CVs for architects and engineers, wrote text for greeting cards, and wrote text that accompanied museum exhibits. There are freelance opportunities like this out there--Craig's List and other writing-related job sites are particularly helpful with this--you just have to be creative in terms of knowing where to look, self-assured in terms of promoting yourself, and willing to take on assignments that you hadn't expected. This helps a writer build a portfolio that s/he can use to get more writing jobs down the line. If you're good with social media, that's a huge plus--many companies look for social media experts and managers to help oversee accounts, and this is one of those paths compatible with an MFA.
While it's very tough to get a full-time teaching job at a college or university with just an MFA, it is possible to adjunct, which sometimes leads to better opportunities in the future (it did with me). I've taught at 7 colleges and 1 high school since receiving my MFA (you can teach at private and charter schools without a teaching certificate), and while it was a bit hectic, I gained valuable experience in these different environments that helped me secure more stable teaching positions down the road.
I too think the stability vs. flexibility issue is at the heart of this question, but in my experience, flexibility leads stability, so I don't think it's always either/or. Thick skin and determination will certainly help, too!