Top Ramen, with 390 calories per package and selling for twenty-five cents, will fulfill your daily calorie needs for $1.25 a day.
Seriously though, I would be surprised if you couldn't put together a balanced if rather dull diet for $156 a month (or $5.12 a day, which now I come to think of it happens to be approximately my daily coffee budget). You wouldn't be eating much meat, but with cereal for breakfast, a simple sandwich for lunch, and pasta or rice + vegetables for dinner I'm sure it'd be sufficient to keep you alive and healthy.
Your daily calorie needs, yes. I think what you'd really be forsaking is not meat (hamburger is relatively cheap) but fresh fruit and vegetables, milk, and most of all, variety. So I'd dispute "healthy." Sure it'll work when you're young, but 10 years of it, and say hi to cancer. And your point about your "coffee budget" just emphasizes it.
In the interest of fair disclosure, I should admit that the reason I had such a low food budget was so I could have more money for beer ;-)
Fresh fruit and vegetables really aren't that expensive. An apple costs, what, fifty cents? A banana, about the same? And you can get a whole head of lettuce or half a bunch of celery for not much more than a dollar. Or potatoes... I forget how much they cost, but it ain't much. As for milk, buy a half-gallon every week for $2.50 and you've got all the calcium you need.
To many people on HN, "fifty cents" for an apple is not that expensive, neither is $2.50 for some milk...I know I easily spend that on a bottle or two of Bawls or 50x that on a new toy for my laptop, or even 100x that on a single nice anniversary dinner at craftsteak in vegas with my significant other while we were in town for defcon (so, hotel and all was even more money). However, 50 cents for an apple earning a minimum wage paycheck working multiple jobs with your spouse to provide for your children while trying to pay the rent and bills is not an insignificant amount of money.
I still remember the congressional food stamp challenge from a year or two ago where everyone who attempted to live on food stamps for a single week made a real point of saying that while it was simple to buy junk food and things like peanut butter, fresh fruits and vegetables, among other "healthy" items to eat, were nearly impossible to buy. Plus even just buying the cheaper junk food, they found that they didn't have the energy they had and always wanted more food...but of course, they wouldn't be able to keep up with the challenge. (http://foodstampchallenge.typepad.com/)
So no, fresh fruit and veggies can be pretty expensive and unaffordable.
I cook every day (it's pretty much a hobby) and almost always spend less than that per month for food. That includes cooking for other people at least once a week and odd recipe experiments. No shortage of meat either... I just finished off a package of chicken tonight that cost $4 and lasted five meals, including one with another person.
I'm having people over for tacos this weekend, pork butt was on sale for $1.50/lb today. One pound of meat makes quite a few tacos, they'll be cheaper than Taco Bell's. And carnitas rules, it will taste like a million bucks. I usually buy what's on sale as it's a good way to stay out of rut, I just make whatever works well with what I bought.
Now I could go buy a piece of kobe beef and spend the $150 in one trip, but for me it's more fun to come up with tasty meals from more basic (but yet good quality) ingredients. If I actually tried to spend as little as possible it could get really low and ramen wouldn't be involved.
I just bought 2 chicken breasts. Price on the package was Canadian $7.50. So say US $6 (guaranteed to be more in SF). That for me, was 2 meals for one, though obviously nice meals (the vegetables, spices, rice probably increased the price of each dinner to about $7-$8 US). So basically I just spent 1.5 days of my budget on 1 meal.
As I said, I usually buy what's on sale (it really is a good way to keep up variety). When chicken breast is on sale it's usually pretty good, in the $2-3.50/lb range which is about half off. Whole chicken is almost always economical. That said, there are a lot of other cuts of meat (pork chops, roasts, etc). After the holidays you'll be able to pick up turkey and ham really cheap. I got a ham last year and threw a party, it was ridiculously cheap and delicious. It's all about being flexible, if you're alright with going with the flow you can get away with spending much less than you'd think.
It's a fun challenge for me and I've come up with some fun recipes as a result. That said, I do splurge where it counts--good quality olive oil, parmesan, fresh herbs, etc. At the end of the day I'm in it for a tasty meal, not a cheap meal.
Seriously though, I would be surprised if you couldn't put together a balanced if rather dull diet for $156 a month (or $5.12 a day, which now I come to think of it happens to be approximately my daily coffee budget). You wouldn't be eating much meat, but with cereal for breakfast, a simple sandwich for lunch, and pasta or rice + vegetables for dinner I'm sure it'd be sufficient to keep you alive and healthy.