You might be able to barely squeeze it in... Maybe you'd have to cut your trip shorter.
Let's see: I'd definitely stay offsite. Select a hotel like Howard Johnson's, Comfort Inn, etc..., that offers free transportation to the parks and free continental breakfast. The transportation will be nothing like Disney's, you'll be annoyed by their schedule and how far from the entrance they drop you off, but at least you're at Disney! At breakfast time, grab extra fruits and goodies for snacks during the day.
I agree with Tar, without tickets you can do it but in tickets alone you'll spend most of your budget otherwise.
Are you driving? Can you camp nearby instead? A local site would charge you peanuts if you have a tent.
...On the other hand, if you just can't make it this year, do what we did: Start saving for next! It took us three years to save up for our vacation this holiday but our plane tickets are Delta rewards tickets, no expenses there. I bought our hoppers two years ago, at lower prices (they never expire if unused), that saved us some more moolah, the kids had the goal to travel all year so saved up money for souvenirs, etc., we paid off our resorts last month , had more time to scramble the bargains and all we have left are hte expenses of our stay. Food and stuff... A couple hundred dollars earned in rewards should give us a few free meals at the Rain Forest Cafe and Red Lobster.
The anxiety was worth dealing with at the end... Good luck