Krishna, getting in line early does not help. When they open at 8 AM, if there is a line, they will put numbers in a hat, and everyone draws a number, which determines who gets to the counter first. And that includes ALL people looking for any permits on any trails.
There are no daily quota slots held back for walk-in requests. However, there are always going to be slots made available due to people coming in to pick up their reservations and dropping off slots due to their friends cancelling out. And then there are also no-shows who have a reservation, never cancelled online, and then don't show up to pick up a permit. The group-size reduction slots are made available as soon as the groups pick up their permits, so it is possible to pick one up soon after 8 AM, and throughout the day. The no-shows become available at 11 AM, and again, if there are lots of people looking to pick them up, a drawing of numbers is held at that time.
No-shows for overnight are made available to start same-day. No-shows for day hike are made available to start the next day. In the past, the day hike no-shows became available at 2 PM, but recently, they have been estimating no-shows and giving them out at 11 AM, even though the reservation-holders have a 12-noon deadline to pick up.
You can get a feel for how many permits are available due to cancellations, drops and no-shows by looking at the Unused Whitney Permits
pages I have maintained.