Major Coleman Young, sitting in his office overlooking the icy Detroit River, is giving his city's sink-or-swim options: he says there is the possibility of even higher taxes for a city that already has taxes four times as high as any other city in the state; there may be new taxes on small items -- nuisance taxes; and then there is the unsavory prospect of legalizing casino gambling, jai alai and horse tracks.

"Let's be straight about this," Young says coldly, aware that Detroit's mobster image will make for some resistance to the idea of legalized gambling. "There's already parimutuel gambling in this state. It's not like we're virgins. . . . If the Atlantic City experience is any guide, legalized gambling would raise property values and bring in $100 million more in taxes per year."

Young's proposal would only be the latest step in Detroit's all-out effort to deal with its financial problems -- problems that stem as much from a once-bloated government as from the sputtering, dying auto industry that has created 20 percent unemployment and drained the tax base. What amazes bond market officials and budget analysts is that Detroit has been able to avoid default, for this city has been figured all but dead for years. It is the most desperate of a string of American cities now grappling with how to pay for the social programs and services that big-city governments have come to provide in the last 20 years. The reason Detroit is the worst case is that it is the home of the auto industry.

When the Presidential Commission on the '80s said the government should help the people who live in cities like Detroit to move south, where the weather and the economy hold a better future, that prompted a great uproar from mayors and others who remember New York, Cleveland, Detroit, Boston and Philadelphia in their glory days. And there were reminders that it is not only big cities that are sliding into the financial abyss, but also smaller, nearby cities and suburban communities -- whole areas of the country. Near New York, for instance, Yonkers and other suburban cities are fighting a shortage of dollars. It is a shortage that strains the states to give more and more money to the cities, and it taxes the federal government as well with the costs for social programs for the unemployed and the poor who are left in the cities with the bad schools, the dangerous streets and the broken-down buses.

"The problem with all the cities," says Walter Stecher, Detroit's budget director, is that for years" -- he motions up with one hand, down with the other -- "costs have been going up and revenues have going down. Somehow you've got to close that gap."

In New York and Cleveland, the governments did fall into default; in Boston, the transit system did close down for a while before state aid came; in Chicago, the public schools were closed for a few days. But Detroit continues to dance along the razor's edge of financial collapse. There is a minimal federal aid here (Michigan is 50th of 51 states, if the District of Columbia is included) and the state government, also hard-hit by the auto industry's problems, can't be of much help, either.

And therein lies the story of a city that has the admiration of bond counselors and budget analysts for its get-tough approach to a financial crisis. Detroit has made the tough decisions on budget cuts, and -- surprise! -- it has made the cuts without much political uproar. This is also a city that pays its department directors in the $35,000 to $40,000 range (instead of the $50,000 range of the District of Columbia) and is fighting to keep what business it has in order to revive the tax base. In one part of town, the city is clearing 500 acres of land of people, churches, homes and the rest for a General Motors plant -- a way of keeping tax dollars in the city.

Those familiar with city budgets say the cities that handle their problems well usually have strong leaders. In detroit, the leader is Coleman Young. Critics and admirers alike say he has juggled, prodded and told his sad story of not having money so often and so well that he has kept the city afloat.

"He's got whites coming back into town after 5 o'clock," says one long-time white city resident, remembering when, after the riots, white Detroiters would flee at nightfall. "And he has made friends with businessmen, with the [Republican] governor, with Jimmy Carter, and he got the Republicans to come here for their convention. Even the labor unions understand that this is war; we've all got to help save Detroit."

Despite those efforts, Young and his city are at the edge of default again. In the last year, the city ran a deficit near $100 million. Young has had to cut public services -- he did away with one museum and last year alone he let 700 policemen go. In a little over a year, 4,000 employees have been cut from the city's payroll.

With the cuts in the city workers and public services, the surprise is that no one is calling for the mayor's scalp. The reason is that people here, having had a ringside seat at the decline of the auto industry, understand that the mayor and the city are really in bad straits with a tax base that is shriveling. They have seen lay-offs in private industry so they don't jump at the news of layoffs in the government. People seem to understand that these are hard times.

City businessmen have also worked with Young, protecting his flank at times, although almost all of them live in the suburbs. Henry Ford II took a large role in building the Renaissance Center, the showpiece of Detroit's urban renewal effort. At Young's urging, James Roche, former chairman of General Motors, and other businessmen founded the Detroit Economic Growth Council. That group published studies showing that city workers were overpaid and the city government was inefficient. Young used the study to cut labor contracts and cut the number of workers. Now the business group is helping to keep businesses in the city with a $5 million fund, the first of its kind in the country, to help businesses expand in Detroit. The businessmen even helped to close two city agencies by taking over all of the city's economic growth efforts.

But the near $100 million deficit for last year remains. "We've cut just about to the bone," says Young. "We've got to get some money."

That's where casino gambling comes in. There's not much choice. The city has had to delay payments to its pension fund and make short-term loans from city banks. Its bond rating is not investment grade, so the market is not an option.

"Even if someone gave us all the money we need to meet out deficit right now, we could still need another $125 million because our revenues keep falling," Young says, hands falling to his side in exasperation.

"We're a foreign land up here," he adds. "You folks in Washington don't realize how bad the economy is . . . what the cities are going through. But it's us today and the rest of the country tomorrow. One of every four workers in the country is in the auto industry."