ok, first, check your knees are flexible enough to do this. my 'codancer' is incapable of sitting on the floor like that, i think it's her articulations that just won't let her. when she tries it hurts.

if that's ok, then i bet this is it. it's hurting your feet cos you have all the pressure on them (the pull from your legs being in that position, and you're using your feet to keep your balance)
what i do is, i try to really push my knees into the floor, rather than my feet. it's tiring, but i find it hurts less, and it counters your body weight better in keeping your balance

my teacher was saying to us (although the class was mostly out of shape older women who already have some injuries/troubles) to not even try it until you are comfortable sitting and watching tv for an hour with your legs back like that. that part of it takes a lot of flexibility, and is something to build up to.
i agree with Kalyani about pushing your knees instead of your feet, that is what my Japanese friend told me she does when performing the tea ceremony (her feet are under her butt, instead of to the sides of her hips, but it's similar) that is how she (my friend) is able to sit in that position for so long without her feet falling asleep etc.
shira.net has a great article about what muscles are used to support yourself. if you are thin-kind of in-shape, don't let it fool you if you're not very, very strong.(i don't know if your strong kind of in-shape or thin kind of kin-shape) in addition to your core (ALL of your ab and back muscles, not just the superficial ones that are easy to get with crunches)(i'm going to try and post a diagram of abs from my exercise class in my album) but also your glutes, hip flexors and quads help to support you. obviously, the quads and hip flexors have to be pretty flexible, and she gives some stretches for them (i LOVE warrior ^_^) www.shira.net/dear-backbend.htm
if it's hurting then stop for a while, build up your strength and try again. you might be (probably are) grinding your spine, and you need that for the living ^_^

Here is a stretch that I do to keep my feet limber. people.tribe.net/60399e1f-...5ed4e849ab I hope this works as a link. if not, let me know.

Also ankle rolls while keeping weight on them to strengtnen ankles. Be very careful to keep control so that you do not accidentally
twist your ankle. Massage your feet regularly. They support you every day! They are the foundation of your dance. I'm guessing that
your feet hurt because they are either not limber enough or not strong enough for that position. Keep working at it. It is hard for me
sometimes due to permanent ligament damage.