Deadline for the second lottery is January 11:
http://www.dnr.illinois.gov/hunting/...eyHunting.aspx
I believe you are now allowed 3 permits.
Check here for remaining available permits:
http://www.dnr.illinois.gov/hunting/...sbyCounty.aspx
Public sites are at the end of the list. They are given in abbreivations that are not always obvious and not alphabetical. You may have to look at a paper application (you can download one on the DNR site-should be on first link above) to get the abbreviations for sites you are interested in. I glanced through the list and didn't see anything left for Clinton (but don't take my word, check it yourself), but Hidden Springs was available for later seasons (3-5). Probably some other stuff in the area too.
We apply as a group every year. First person is the group leader, all others have to enter the leader's customer number in their application (a box will appear on the website when you check "join a group"). I don't think it gives you any advantage or disadvantage.
Good Luck.