It is definitly a possibility. During the busier times they run out early afternoon.
If they do run out of them before you get one and you dont mind being seperated from your party you can do the single rider option. I did this in Aug 2003 when the wait time was estimated at 90 mins and got to ride in about 10-15 mins. In Dec 2005 the wait was estimated at 45 mins and I got through in about 5 mins each time.
Just ask the fastpass attendant for a single rider card.