Walk-ups should be relatively easy to get. Right now, most dates are reserved for July and August, but that is 36 slots, and 24 more are held back for walk-in requests.
If you are at any Inyo N.F. ranger station (there are 4) at 11 AM the day before, you are sure to get a slot. (Call the wilderness permit office to make sure of that 11AM day-before time. 760-873-2483)
Steve, Kurt Wedberg posted on the FB group that RecDotGov website is not able to release No-Show reservations for Walk-ins. If someone doesn't show, and doesn't cancel, that quota spot goes unfilled. Cancellations are handled online, so that means Walk-In options are going to be screwed up until this gets fixed. Its not clear what the problem is, but since software is your field, you might have some insight on what's going on.
And since there's no refund for cancellations, people are not motivated to go back online to cancel them. But that's the solution they're proposing for now, people need to cancel if they've not going to use their permit. Its now become a duty to cancel your reservation, not just a nice thing to do.