So that means they may put you in the 10 a.m. lottery for any unclaimed overnight permits for entry that same day (or, if they have a ton of unclaimed permits, they may just rewrite your permit). They'll have everyone pick a number out of a hat, and they'll call you by number and give out permits until the permits are exhausted. If there are more permits than people who want permits, everyone wins.
For a Wednesday at the end of June, you have a good chance. Last year, there were 25 unclaimed permits for the last Wednesday in June meaning that, even after the same day lottery, there were more permits than people who wanted them. See
http://www.whitneyzone.com/wz/ubbthreads.php/topics/3436/Unused_Whitney_Permits_2010.