Great discussion here. I have an insiders perspective to add as an employee of the company behind the Go Chicago Card that hopefully is of help.
It definitely would be tough to do most or even half of the things included in the card in 3 days as modeche points out. We set the program up so you don't have to do anywhere near that much to get value. As tomfromal's quick math shows, most people do a few things each day and save a bunch in the process. And in terms of special exhibits that might come with an extra fee -- those extra fees are added to regular ticket prices too.
If you are time constrained -- and especially if your kids at the age where standing in line is torture (that's where I am with my kids), then the skip the line privileges that pgo mentions are invaluable. For example, the Shedd is a must see for many people, but as a result can get pretty substantial lines (60 minutes or more is not unheard of in the busy months). And being able to grab the hop on/hop off trolley included with the Go Card can be a handy way to get around among the key sights.
It sounds like tomfromal intends to do a variety of things so the Go Card is probably a good fit. For anyone looking to only hit a few places, the Chicago Explorer Pass (pick 3 things from a list of 28) is another option worth looking into. Hope that helps -- have a great trip!