I'm from Ohio, and spent some time in Illinois many years ago, in the Air Force (Chanute AFB, Champaign-Urbana.) I'm a little surprised that there aren't any readily-available water sources - in the well-watered eastern US, there's usually a stream, pond, or spring you can filter water from. It's especially odd that, if they have established an elaborate system of backcountry sites, that they haven't made provisions for water sources.

There are really too many variables for me to estimate how much water you'll need. These include whether you normally drink more of less water, how hot it will be (you need more water at 89 degrees than at 60), how fast and hard you'll be walking ((uphill? Downhill?) how you cook (freeze-dried versus from-scratch; freezer-bag versus dirty pots that need washed), whether you want additional beverages with your meals, and so forth.

Having said that, I can tell you that in southwest Ohio (or at Shades Park near Crawfordsville, Indiana - just short of Illinois), I'll drink 3 liters of water during the day's hike (including lunch) on a 75-degree day with an 8 -10 mile hike. I'll use another liter for breakfast, and a liter for supper, plus a liter overnight and to the first source the next day. That's a total of six liters a day - for me. You need to think about your own needs.

One alternative to carrying 12 or more liters of water would be to cache water. Often, trails will cross a road near a campsite, or there will be a short service road the park uses for maintenance of the backcountry campsite - store your evening and second day's water just inside that road, then go get it after you set up camp (your empty pack can easily handle a couple of gallons.)

Another alternative, depending on where you are in Illinois, is to get your passport in order and go to Shades Park in Indiana. The trails are beautiful, you can adjust the length of your hike to suit your needs and the weather - and there's plenty of water, both from fountains at the picnic and parking areas, and from the plentiful streams if you filter. There's even a spigot (and a really nice latrine) at the backcountry campsite (about a two or three mile hike from the nearest parking lot). If you're not quite sure how to gauge your water needs, and sources are uncertain or non-existent, you might be better off to take your first trip somewhere that has reliable water. That way, you can get a feel for how much water you use, without having to worry about how much to carry or cache.