You need to be responding to interview offers in a matter of hours (like 2-3, not 24-48). If you don't have a Blackberry/iPhone/Android/whatever that checks your mail constantly, you need to be checking it every 3-4 hours during interview season (9/1 - 2/28 or so).
Interview invitations go like hotcakes. You need to get on the calendar ASAP. Programs are more likely to change an interview date than they are to offer an "overbook" spot to somebody who put off scheduling.