30 bucks for snacks in the park would go a long way with our family of four, would maybe not last for a whole 10 day trip, but for a 5 or 6 day trips, we absolutely could make it work. And if that was the budget for 10 days, we could make that work also. We bring in snacks and do the crystal light in the waterbottles. If we want to go every year or so, we need to budget. We do not get junkfood/snacks daily. We all pick a couple of gotta haves and that is what we get. example, I love dole whips so I get one of those, DS and DH loves icecream mickey bars, they get that, dd likes that way way way overpriced colored flavor sugar in a tube from the Downtown Disney candy store, so she gets that. See we all get what we want, just not every day. Why pay 6 bucks for popcorn when I can make it back at the room for MUCH less. Why pay 3 bucks for a soda when crystal light in a water bottle will quench your thirst better. We still have lots of junk food, but we hold our cravings for the room and pigout on soda, candy and popcorn there

. if we must.
I know a lot of people feel they are on vacation, lets live it up, and we do to in our minds, but moderation is the key for us. We would rather save our pennies to go more often than have a blow out trip. And this is from our experience....we had a luxury trip a few years back not at disney but somewhere else, and we decided it was not for us....nothing we did was ultimatly worth the cost. Yes the food was good, but was not worth the price we paid, hotel was gorgeous, but it was at the end of the day a place to sleep for a few nights. .
But we realize to each their own, we have friends who it is not a vacation unless they stay at the fanciest of resorts, eat the fanciest of foods and every whim of an 6$ premium icecream cone is fulfilled. So they go for a blow out long weekend/short week every year. We take many smaller weekend trips and at least one larger 10 day or so trip every year, some years we manage one large and one medium (5) day trip. We can usually do all of that for what they spend on their one luxury vacation.
Our kids learned from an early age that they are not getting everything they want. We go to disney to see the sites not to shop for the most part, so we simply do not spend much time in stores, that cuts way back on the "i wants". We do Tinkerbell gifts everyday at the room, so they know they will be getting a special treat so they feel special (I pick them up all year long at sales, dollar stores etc....and we have found that a simple piece of candy is usually the thing they are most excited about anyway).
None of this feels "budget" to us as this is how we live day to day. It feels luxurious to our kids cause they got a overpriced sugar tube , mickey icecream bars and a special tinkerbell treat left on their pillow each day in addition to riding roller coasters and visiting Mickey.
Again, this works for us and is our philosophy, we go for lots of experiences instead of one "luxury" trip. We have done the luxury thing and frankly it was not worth the money to us. We are happy seeing the castle without a 6$ snack in our hand, others need the snack. To each their own, it is a wonderful thing.
However the question at hand is can you do disney for 3 grand or under.....my answer is yes you absolutely can.