Hate to sound cynical, but here's what I see happening if this gets passed:
The day after it goes into effect, a random TFLer from (for example) Indiana straps on their piece and drives to Chicago. Our protagonist is smiling and walking down the street when a police officer happens to notice them printing.
"SIR! Keep your hands where I can see them and turn around to face the wall. Down on your knees, cross your legs and put your hands on the back of your head. I'm going to disarm you now. Do you have any other weapons or drugs on you?"
Befuddled, the TFLer responds. "Huh? Oh, well I've got my pocket knife ... and in addition to the 1911 you've already taken, I keep a Kel-Tec in my front pocket ... but officer, I've got a permit to carry a handgun, it's in my wallet. Due to the passage of new federal legislation, Illinois must now accept my Indiana permit and I believe I am in full compliance with the law."
Here, the officer snorts as he roots around in our TFLer's pocket for the Kel-Tec, dropping the magazine as he pulls it out. "So youre one of those huh? All right, well I see your federal law and raise you Illinois' brand spankin' new list of prohibited places for handgun carry. And I quote: 'No individual outside of Law Enforcement or other government service who possesses a permit to carry a firearm may carry a handgun or other weapon in or about the vicinity of:
Any bar, liquor store or commercial establishment that serves alcohol.
Any church or place of worship.
Any non-interstate public road.
Any playground, park, school, school zone, daycare, school activity, university or business that caters to children.
Any public sidewalk or pedestrian crossing.
Any vehicle of public transportation.
Any athletic facility.
Any bank or financial institution.
Any police station, fire station or hospital.
Any government office, government building or government-owned, leased or rented property.
Any hotel, motel or other temporary lodging.
Any apartment building or complex with more than 10 residents.
Any public parking lot.
Any commercial establishment that does more than $200 in gross sales in a day.'
Pal, you were in violation of at least half a dozen of those when I caught you. You're under arrest for carrying a handgun without a permit. You have the right to remain silent..."
I'd give the statists no more than a few months before every state that already lacked concealed carry laws had a similar set of prohibited areas for carry. Hell, I bet a few "may issue" places would set up something similar.