I live in one of those counties. It had an almost 80% in favor of starting a separate state. 

Biggest complaint I know of is elections. Even if everyone outside of Cook Co (aka Chicago) voted the same way, the vote from Cook Co could still outvote it. So basically it amounts to "what's the use in voting if you live in "downstate" IL? Then, add what they call the collar counties, those bordering Cook Co, and you find the folks that either fled Cook Co, or would like to live in Chicago, but rather value their lives more, and you are really outvoted downstate.

Our present governor is from Cook Co. Our recent past POTUS claimed he was from Cook Co also.