Hello bulldog34,
I work as a Wilderness Ranger on Mt Whitney.
Think of the old apples and oranges analogy.
The daily entrance quota for overnight permits is 60 per day, whereas the quota for day hikes is 100. This means that overnight permits are more difficult to obtain. In all fairness to those people who really want to do an overnight hike, you need the appropriate permit that reflects your itinerary, i.e. a day hike permit.
I realize that currently there are no day hike reservations available for the 18th, however the Resevation Office will often get cancellations and/or reductions in group size notifications around five days prior to a trip.
In addition,there are either cancellations, no-shows, and/or reductions in group size that occur daily when people come in to pick up their permits at the Visitor Center in Lone Pine. Those freed quota spaces are then obtainable on a walk in basis.
I would suggest contacting the Reservation Office at (760) 873-2483 around 5 days prior to your Whitney hike. They will help you convert your apple to an orange for free if space is available which often is the case. If not, you still have a decent Plan B which is to come into the Visitor Center in Lone Pine the day before your hike. It may take a couple tries that day but you have a very reasonable chance of obtaining the desired day hike permit.
Good Luck
Dave Kirk USFS Wilderness