This city, recently acclaimed (to much mirth elsewhere) as the nation's most livable, is looking down the tracks toward a mobility crisis.

The Pittsburgh transit system's managers are drafting a plan to stop running all 900 buses, 90 trolley cars and 10 commuter rail cars that together carry about 150,000 Allegheny County riders every day.

Unless something happens, Allegheny County Port Authority Transit (called PATransit) will run out of money in June and cease operations indefinitely, its board of directors has decided. Although an element of political gamesmanship is involved, there is a money shortage.

The fact that Pittsburgh is planning such dire action is cited in Washington by the American Public Transit Association as the sort of thing that happens when the federal government reduces aid for public transit.

But the feds do not get all the blame. "Our problem is simple," PATransit board chairman James C. Roddey said. "We don't get enough support locally."

The problems are related. Cities across the nation have used federal transit aid to buy buses, build trolleys or heavier-duty rail systems and refurbish maintenance facilities. Though the federal government provides up to 80 percent of the cost of those facilities, since 1981 it has been reducing its aid for operating costs, mostly labor. No system covers its costs through fares.

Federal operating aid now runs between 4 and 10 percent of total budget for most big-city transit systems. In Pittsburgh it is $10 million, 7 percent of the budget; at Washington's Metro it is $18.5 million, 4.6 percent.

The Reagan administration's original budget proposed to eliminate operating aid to transit systems in fiscal 1986 and to cut funds for new buses and trolley cars from $4.1 billion to $1.4 billion. The budget agreement between the administration and Senate Republicans would do the same thing, but over five years.

The Allegheny County Commission, which owns PATransit, is like many other local governing bodies: It must finance everything with the politically sensitive real estate tax. Although the state legislature's support of transit has grown steadily, no Pennsylvania county has been granted the right to establish a local transit tax to help pay the system's costs.

Thus PATransit, Urban Mass Transportation Administration chief Ralph L. Stanley said, "is a good public transit system that has gotten ahead of its local funding base."

Stanley sees similar trouble in Buffalo, Miami and Washington, cities that have made major (mostly federal) investments in new transit construction but have not nailed down a reliable tax source to supplement fares in defraying operating costs.

A few cities, including Atlanta, Dallas, Houston and Seattle, have dedicated transit taxes. But most cities pay for transit the way Washington Metro does: with a combination of state and local aid subject to the annual uncertainties of the budget process.

Stanley and his predecessors have had some success in persuading Congress to require cities to prove that they can pay for operating a new or expanded rail transit system before the federal government agrees to help build it.

The argument about whether transit is needed has largely ended at the big-city level. Even such automobile-oriented cities as Los Angeles and Houston are planning major transit expansion. But federal aid for public transit is sharply attacked by the Heritage Foundation and other conservative groups, which say that too few people use public transit to justify its financing.

Ridership figures alone distort the picture, however. The time of day people use transit and the destinations mass transit serves are more important indicators.

For example, in the Pittsburgh Point -- where the Allegheny and Monongahela rivers meet to form the Ohio River and the heart of Pittsburgh's bustling and rebuilding downtown -- three of every five people who go to work during rush hour get there by public transit, as do half of all the people who shop there.

In central Washington -- including downtown, Capitol Hill, Crystal City, Rosslyn, the Pentagon and National Airport -- half of the rush-hour travelers ride Washington Metro. Rush-hour public transportation ridership is 80 percent in Chicago's Loop, more than 90 percent in lower Manhattan. Even in Dallas, where the bus system is small (although expansion is planned), transit riders represent one-third of the people who go downtown in rush hour.

Pittsburgh has put its federal transit dollars into a modest rail system and the construction of buses-only expressways along existing railroad rights of way.

The $113 million East Busway, opened in 1983, runs 6.8 miles from the suburb of Wilkinsburg to the heart of downtown and cuts rush-hour travel time from 40 stop-and-go minutes to a smooth 13. Express buses run every three minutes during rush hour, and six stops along the way serve dense residential neighborhoods.

PATransit is about to open a $559 million subway, a tunnel to get its trolleys off the narrow, crowded downtown streets. New trolley cars have been purchased to supplement the fleet. PATransit's buses are in their best shape in years.

For PATransit's current budget year, which ends June 30, Executive Director William W. Millar proposed a $149.6 million budget, which would have permitted him to open the subway before June. The County Commission would not approve those funds.

At $1, Pittsburgh's base fare is one of the highest in the nation, and the transit board did not want to revisit that issue. The only solution was to find cuts.

The subway's opening was postponed until after July 1. No new mechanics or bus drivers have been hired to replace those who have left. "We're missing trips due to that," Millar said. "You save money in the short term, but it catches up with you."

PATransit proposed a 37 percent service cut that would drop many trips, eliminate some routes and reduce night and weekend service. Roddey, a businessman who agreed to take the nonpaying transit board chairmanship, says that he will never forget the public hearings on that idea.

"I came home one night after a 13-hour public hearing where 158 people spoke," he said. He said those people complained that if the cuts were imposed, "I'll have to give up my job," or "I'll become a shut-in" or "I can't go to church."

About 10,000 people wrote the transit authority to complain.

On the recommendation of a citizens' advisory panel, the board decided to operate the full system until there was no money, then close it in a rational way that would preserve it until it can be reopened. This obviously puts pressure on the three-member Allegheny County Commission, which has endorsed enabling legislation from the state legislature for a local transit tax.

Roddey has come to believe that transit is a legitimate taxpayer-supported service. A 1983 survey found that more than a third of PATransit riders had household income of less than $10,000 and that 22.5 percent of them were between ages 15 and 24 and 22 percent were older than 64.

"I don't think the federal government belongs in operating subsidies," he said, though he asserted that the federal government "created addicts, and now they want everybody to go cold turkey, with no methadone program."