I think there are two types of Walk-up permits.
Those that are set aside as walk-ups in the overall quota.
and those that are reservation no shows, and get released as walk-ups.
My experience refers to walk-ups as part of the quota.
these are permits for next day entry.
I got SOBO JMT walk up permits out of Yosemite Valley (not Tuolumne) in both 2007 and 2008 during early August. It was not a big problem as long as I got in line very early ... 5 am, 4 am , depends. Anyway I got a permit both times.
Solo permits are easier to get than one for several people, since the quota is not large, first come first served.
Tuolumne can't be that much different, but check on their quota.