It can be done, and you don't have to be superhuman to do it.

My friend in San Francisco wrote this blog with some good ideas.
http://cooking4theclueless.wordpress.com/2010/07/02/you-can-eat-locally-organically-on-a-budget/

I wish I knew where to buy mutton around here! The cheapest healthy meat I can find is ground turkey, which is quite versatile. Free range beef is a bit more expensive than regular, but that can be dealt with by eating a bit less of it (the benefits will be greater than eating more of the grain-fed kind), and by using up every bit you buy. You can also buy it in bulk from local ranches, for some savings, as long as you know you'll use it up and you have room for it in a freezer.

Another point is that avoiding processed and pre-made food also saves money. This is especially true for gluten free and specialty food, it's much cheaper to make from scratch.

You can fill up a cart with produce pretty cheaply, and some produce doesn't have to be organic. The top twelve LOW in pesticide produce items are:
Onions
Avocado
Sweet Corn
Pineapple
Mangos
Sweet Peas
Asparagus
Kiwi
Cabbage
Eggplant
Cantaloupe
Watermelon
Grapefruit
Sweet Potato
Honeydew
Melon

The following twelve should be bought organic:
Celery
Peaches
Strawberries
Apples
Blueberries
Nectarines
Bell Peppers
Spinach
Cherries
Kale/Collard
Greens
Potatoes
Grapes (Imported)

You can download a pdf or an iphone list here: http://www.foodnews.org/walletguide.php

It can be hard to find super fresh organic produce, at least where I live, but food co-ops are becoming more numerous and many offer organic (or local organic standard but not certified) options. I've found the one that I tried (Community Food Co-Op of Utah) to be very fresh and good. I just finished off the lettuce and spinach from last Saturday and it was still fresher, cleaner and tastier than anything I see in stores. (I did clean and spin it dry on Saturday and then stored it with a paper towel in a bag in the fridge to keep it fresh.) The radishes were gone almost instantly (I'm a fan of radishes, they're good for explorers, and these were beauties). I still have a couple heads of fresh garlic to work on, and the share included a potted herb that I planted in the yard last night. Their regular share is also a great deal and includes more variety at this time of year. In this area, Bountiful Baskets is another good option. I haven't tried them yet, but have heard good things.

It also saves money to stop eating out almost entirely. Restaurant food is never as healthy as homemade and it usually isn't any faster by the time you decide and go and order and wait, etc.

Of course the other key is just to avoid waste. Healthy foods are easy to re-use and come up with tasty results. It's not hard to scramble some eggs and add some leftover meat, rice, veggies etc. Soup is also an easy and way to reheat simple leftovers. Broth, onions, ume plum vinegar and seaweed are always a good base. You can add fresh veggies into the soup (like carrots or celery, and raw veggies on top (like green onions, sprouts, avocado, whatever). Salads are a great way to use up leftover steak and veggies as well. With a few basic recipes, you can go a long way toward reducing waste without getting bored.