The last time I remember budget cuts, they went something like this...
Magic Kingdom was open 9-9, but the openings of some attractions were staggered. Not all vending carts were available, nor were some quick service, and it depended on the projected attendance. Fewer castmembers were scheduled and asked to cover more tasks. Part timers were not scheduled unless absolutely necessary, full timers weren't getting their full 40 hours and College and International students were covering the areas. The instituted a hiring freeze.
At Epcot, Future World opened at 9 and closed at 7 pm, and World Showcase ran 11-7. Not all food stands were open and the times were staggered. Evening shows didn't run every night.
Hollywood Studios also staggered openings if shops sold redundant things and could be bought else
where in the park, those shops may have been closed. Nightime shows only performed a few nights a week, there weren't as many show times scheduled and Streetmosphere was not always our. As in the other parks, castmember hours were cut and and some food and beverage places weren't available. That park usually closed at 8 pm.
At Animal Kingdom it was more of the same listed above, and they were open from 8-5.
Some of the entertainment in the hotels was cut back in number of shows per week,
At that time, Downtown Disney was still operating and the hours were staggered depending on if you were in Marketplace, West End or Pleasure Island.
The waterparks also operated on shorter hours.
Hopefully this doesn't come to pass. With a new theme park opening less than 20 miles awsy. But at least this can give you an idea of what has happened in the past