Unfortunately, that is not how it works. If you're applying in a field smaller than medicine or peds, the interview spots can fill up quickly. And the more desirable the program, the faster the spots fill.
I try to get back to a program within about 4 hours. Later than that, and you may not get the date you want. And I wouldn't count on being able to reschedule.
It helps to plan ahead: block off a period of time to interview in each region you're considering, and then when the interviews start rolling in, choose the date that works best with your plan. You may find that you're able to save substantial money that way by driving within the region instead of flying.
Or, alternatively, book all your interviews, and then, when it looks like you're mostly set, book your flights as a multi-leg trip. It really does save money to do that, instead of flying home after each interview. It's also cheaper to rearrange your itinerary from the airport to include an extra stop, than to book a whole new trip.