(CBS News) CHICAGO - Last December, minutes after he allegedly shot at a neighbor, Julian Gayles was caught by Chicago police. Gayles, 22, already had a record of gun crimes and parole violations, but had spent little time behind bars. Since 2009, he has been sentenced to seven years in jail, but has served just two.WATCH: Obama mourns "a Newtown every four months," below
Gayles was on parole when CBS News witnessed his arrest by police commander Leo Schmitz and is now in custody again, awaiting trial.
Chicago police superintendent Gary McCarthy wants such offenders to face a mandatory minimum sentence.
"This has to stop," McCarthy said. "Gun offenders have to do significant jail time."
Chicago already has some of the toughest gun laws in the country. This week, Mayor Rahm Emanuel called for making them even tougher, with minimum mandatory sentences for gun violations.
But Cook Country Sheriff Tom Dart says he doesn't have the cells to hold more inmates.
"I mean, we are at capacity right now," Dart said. "The state prison system is beyond capacity. You talk to them right now, they haven't had a population like this in decades. And there's no place to put 'em."
Dart runs the largest county jail in the country. Nearly 10,000 inmates -- including 300 prisoners -- living in a former cafeteria and some sleeping on the prison hospital's floor.
"This is not something that you would design, " said Dart. "Frankly at this time this should be a building that we should have empty right now at this time of the year. There should be no one in it. But because of our population explosion, this is full."
Experts say the prison population would swell by thousands if mandatory minimum sentences came to pass for gun violations.
"We can't have this irrational type of notion that there's magic jail cells all over the place that are all sitting there empty, " said Dart. "It's as if all of a sudden we just raise penalties and these people get shipped off to the moon or something. It's like, 'No, we know where we need to put 'em,' and we need money to fund that."
But Illinois doesn't have the money and has actually been closing prisons to save money so it can reduce the $9 billion it owes in unpaid bills.