For many American cities, the Great Recession is a fading memory. Others feel the damage it inflicted every day.

Across the nation, cities like Boston or San Francisco that are blessed with vibrant high-tech industries churning out high-skill, high-wage jobs, all but escaped the downturn.

And then there are the broken cities. The hardest hit find themselves in a deep downward spiral of declining services, rising crime rates and falling property values. Some have or are contemplating filing for municipal bankruptcy – a drastic step with uncertain results. What's worse, the struggling cities are like a weight dragging down the rest of the economy. (Infographic: See how your city is faring.)

Once a city is badly broken, it can be very tough to fix.

Just ask Darren Green, president of a coalition of community groups in Trenton, N.J., where deep budget cuts two years ago forced the city to lay off a third of its police force.

"We're at a place now where it's very dangerous to walk the streets," he said, his thoughts periodically interrupted by the distant sound of passing sirens. "The school system is dysfunctional and not working. You have young people who are robbing elders. Young people who are destroying communities. With no leadership and the community in disarray, there's a lot of bad here."

The disarray and mayhem in Trenton is extreme. In August, the city set a record for the most homicides in its 221-year history. Trenton's mayor, Tony Mack, has asked the state for emergency funding. But his appeal has been undermined by allegations of corruption after a federal grand jury indicted him in December 2012 on bribery charges. Several key members of his administration also have been charged with other, unrelated crimes.

The plight of the Garden's State's capital city is by no means typical of American cities in 2013. For the most part, these regional economic hubs held up relatively well after the Great Recession tore one of the biggest holes in local revenues since the Great Depression.

The high-growth local economies in San Francisco and Boston have recouped the ground lost to the recession and continue to help push the national recovery forward. Others hit hard by the housing bust, like Orlando and Phoenix, have recovered as the housing market has revived.

Innovation has also helped revive once-stagnant local economies. In Chattanooga, a newly-deployed high-speed Internet network has become a magnet for foreign investment. The southern city once known for making Moon Pies is now a model hub for the smart grid and one of the fastest-growing cities in America.

But as the national recovery sputters along, some cities are being left behind as tight budgets and lingering damage from the Great Recession continue to challenge city halls across the country. As the source of more than 90 percent of U.S. gross domestic product, the strength of that national recovery will be determined largely by the success of American cities in overcoming the challenges to short-term recovery and long-term growth.

Those challenges loom large. By 2009, the Great Recession had pushed all but four of the 384 local economies tracked by Moody's Analytics' Business Cycle Index solidly into reverse. Of these, 255 moved into recovery in 2010. But as of August, the latest month for which data are available, another 73 are at risk of sliding back into recession. Since 2010, eight cities have filed for bankruptcy including Detroit, Scranton, Pa. and Stockton, Calif.

The hardest hit cities find themselves mired deeply in downward spiral, as cuts in services, rising crime rates and falling property values all contribute to the decline.

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"If you can't provide the environment for investment, the process of shrinking just continues," said Jeffrey Keefe, a labor economist at Rutgers University. "The people and businesses leave, and there's no inflow of economic resources. So all you're doing is living off external subsidies to provide law and order and some basic education and social insurance."

Since the Great Recession ended, there are now a half million fewer municipal workers patrolling streets, teaching kids and fixing potholes, according to the U.S. Bureau of Labor Statistics. Their disappearing paychecks have further drained local income and sales taxes.

Lost spending by local governments has also hampered the national recovery. Fueled in part by a surge in real estate taxes, state and local government spending grew by about six percent a year from 2001 through 2009. In the past three years, however, that growth has slowed to less than 1 percent a year. The difference amounts to about $450 billion over that period, according to data from the U.S. Bureau of Economic Analysis.

Trenton's decline has been slow in coming and will take time to reverse.

The city has deep roots. George Washington is said to have chalked up his first Revolutionary War victory here. The city briefly served as the nation's capital. For the next century and a half, Trenton grew steadily as a thriving manufacturing hub. On the city's South Bridge, the first built over the Delaware River, bright neon lights still proudly proclaim at night the slogan cooked up in 1917 by the local Chamber of Commerce: "Trenton Makes, the World Takes."

But Trenton stopped making things many years ago. The city's economic decline has tracked the decades-long ebb of American manufacturing might. Today, state government is the largest employer – but the government presence does little to help balance the city's books.

Some state and federal officials argue that cities need to be run more like a business. But unlike a private business that can exit markets or consolidate product lines when times are tough, a city grappling with a 20 percent drop in revenues can't just decide to ignore every fifth 911 call, or plow only 80 percent of city streets.

Perversely, ongoing budget cuts in declining American cities can force up the cost of running local government. High unemployment brings increased demand for social services —from packed homeless shelters to police response to increased crime. Years of deferred maintenance on infrastructure like roads and sewers only accelerates the need for costlier replacement.

For the most part, though, taxpayers are in no mood to pony up more money to offset those costs. That presents local political leaders with a tough balancing act if they want to develop long-term solutions and continue to serve through the next election.

In good times, local governments looked to plug budget holes with state aid, which once accounted for as much as a third of local government budgets. But those funds have also shrunk after states took their own income tax and sales tax beating from the Great Recession. Some three dozen have gone further to tighten local revenues, by enacting so-called Taxpayer Bill of Rights laws that cap the level of tax increases local governments can impose.

In better times, Uncle Sam also used to provide generous federal funding for job training, community development block grants and public housing. But local officials complain that has been replaced by unfunded mandates for clean water and higher school test scores.

That has left many of America's most distressed cities to fend for themselves. "The resources are there; the question is whether they can be reallocated from the communities that have resources to those that don't," said Keefe.

It won't be easy for America's most badly broken cities to bootstrap themselves back to prosperity. But with the right political leadership, it's not impossible, according to Bruce Katz, founding director of the Brookings Metropolitan Policy Program.

"Thirty years ago, we thought Boston was dead. We thought New York was dead. We thought Pittsburgh was dead," he said. "All these places have sprung back to life. So if you're left behind in the near term because of misguided political leadership, in 10, 15 or 20 years you might find a very different kind of political environment."

In Trenton, community leader Darren Green agrees. "Trenton is a phenomenal city," he said. "It has a lot of great history; it has a lot of great people. It just needs leadership that is committed, competent and caring."

"We're going to rebuild this city," he said. "I promise you that."

—By CNBC's John Schoen. Follow him on Twitter@johnwschoen.



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