On a recent evening on Chicago's southwest side, an all-too-familiar scene unfolds: within sight of the Windy City's iconic downtown high-rises, dozens of police officers swarm. A 21-year-old man has been shot outside his home.

All of a sudden, a deafening scream pierces the silence: the man's family has just learned he has been declared dead at the hospital.

Chicago -- the Midwestern stomping grounds of Al Capone, the ruthless mobster who left a trail of blood in the Roaring 1920s -- is grappling once again with a gun violence problem and a soaring murder rate.

There have been more than 670 murders in Chicago from January to mid-November, according to police -- a 56 percent jump in just one year. The city is on track to end 2016 with the most killings since 1998.

On Friday night, the grandson of Illinois congressman Danny Davis was fatally shot in the head -- over a pair of shoes, police said.

The nation's third largest city is struggling to figure out how to stem the free flow of bullets and blood, and is hoping new, tougher gun laws are the answer.

"I have seen too many lives torn apart. Too many parents lose a child," Chicago's police chief Eddie Johnson said at a recent public forum.

"As a Chicagoan, I'm ashamed, because we could do better."

- 'Beyond frustrated' -

Johnson and his state lawmaker allies want to reduce the number of shootings by stiffening jail sentences for those repeatedly arrested for gun offenses.

The police department says that a hard core of 1,400 recidivist gun offenders -- many of them gang members or drug dealers -- are fueling much of the violence.

"We're beyond frustrated," said Anthony Guglielmi, a police department spokesman. "You could reduce the violence in the city by 40 percent just by keeping people in jail for crimes they have committed."

The new draft bill is headed for the Illinois state legislature in the next few weeks, where there are indications of bipartisan support.

It would ask judges to sentence repeat gun offenders at the higher end of the three-year to 14-year guideline range. Judges who hand down lighter sentences would need to offer a written explanation of their reasoning.

Despite a tough national climate for passing gun control measures, the bill's authors are hopeful that Illinois will be different.

One reason is that the state's Republican governor Bruce Rauner has already agreed to tougher gun laws.

Earlier this year, he signed a bill to increase penalties for gun trafficking from nearby Wisconsin and Indiana -- border states with more permissive gun laws.

Another reason is that this latest sentencing law would not impose strict mandatory minimums, something legislators and gun-rights advocates have opposed.

"Illinois can be a real trend-setter here," said state representative Michael Zalewski, a Democrat who supports the measure.

Republican state lawmaker Michael Connelly has also offered cautious support, saying, "We have to do something."

- 'No employment, no resources' -

But officials admit that tougher gun laws cannot fix the deeper problems at the root of the violence.

Alicia Means, 42, lives in the struggling Marquette Park neighborhood on the city's southwest side.

When she hears the sounds of gunshots, she says, she and her children drop to the floor inside their home, just in case a stray bullet pierces the walls.

Life was not always this way. Growing up, she said her neighborhood was "nice and clean... People cared about other people's children."

But the housing crisis and Great Recession took a toll on the streets around her, where there are now a number of abandoned homes.

"Change has been mainly no employment, no resources, people losing their homes... no way to pay their bills," Means said.

Alex Kotlowitz has heard all of this before, having spent decades studying Chicago's economically-challenged neighborhoods. His book "There Are No Children Here" takes an unblinking look at growing up poor in Chicago.

"There are a lot of reasons why there is violence in what is a fairly concentrated part of the city," Kotlowitz said, citing historic socio-economic factors and trauma from past bloodshed.

But he says longer jail terms are not the answer for predominantly African-American communities that "have faced longer and longer sentences in every crime imaginable."

"There's a kind of tone-deafness about it," he said. "The idea that this is the premier solution that people are talking about, for me, is just so disappointing."

Johnson, the city's police chief, who is black, insists he understands the pitfalls.

"I want our focus to be on individuals that we know are driving the violence on the streets," he said.

"The last thing I'm looking to do is lock someone up based on the color of their skin or where they live."