This was once the city of perpetual motion, an economic engine that was the envy of the nation, a symbol of the rising Southwest and, some Houstonians boasted, a model for the American city of the future.

Houston could become that model someday. But for now, economic hard times and a fractured political consensus have brought a new humility to leaders of the nation's fifth largest city. After more than a decade of growth and prosperity, confusion has replaced confidence:

* Mayor Kathy Whitmire, elected overwhelmingly as this city's first woman mayor in November, 1981, is increasingly under fire and faces a well-funded opponent in her reelection bid this fall.

* Business leaders, weary from a recession that has left Houston's economy in the doldrums, are getting their way less and less and are losing enthusiasm for tackling the city's problems.

* Voters are showing that they are losing faith in solutions proposed by their leaders.

All of this came to a head on June 10, when a proposed $2.35 billion bond issue to build the first 18 miles of a rail transit system was rejected in a public referendum by a margin of almost 2 to 1.

The defeat stunned many Houstonians. The city's freeways are congested daily from 7 a.m. to 7 p.m., and transportation consistently shows up in surveys as the city's No. 1 problem. Polls had shown 60 percent of Houstonians supporting an all-rail system and 70 percent favoring a bus-and-rail system.

Moreover, the bond issue was supported not only by the Metropolitan Transit Authority but by Whitmire, 11 of the 14 City Council members, the Chamber of Commerce, a host of business organizations, leaders of the black and Hispanic communities and the city's two newspapers. In opposition was one outspoken City Council member and a few under-funded civic organizations in Houston's outlying areas.

"It's a humbling experience to take a licking like we did," said Alan Kiepper, Metro's general manager, who was brought to Houston from Atlanta a year ago.

The defeat may have been little more than a rejection of what appeared to be a costly boondoggle serving too small a fraction of the population.

Or voters may have been registering disapproval of Metro itself, which has by far the worst image of any city institution, and the board of which is considered arrogant even by rail transit supporters. Well before the June vote, it agreed to purchase the cars for the rail system--from a Japanese firm--and it held at least one public meeting at a private club.

But although city leaders caution against reading too much into the transit vote, interviews with a number of Houstonians in public and private life suggest that it came at a crucial point in Houston's history. Many are wondering whether they still can create something special in this steamy city that some people believe should never have been created in the first place.

Behind all the pessimism is Houston's economy. Despite evidence of recovery nationally, Houston is expected to improve more slowly than other areas because of its dependence on the oil industry. Unemployment here is still about 10 percent.

For the first time, surveys show that the economy is the most important personal issue for most Houston families. Only a few years ago, the economy did not even register as an issue in most surveys.

The slump also has altered the psychology of Houston, for it was the economy that drew many people here initially. Now polls show that many Houstonians would leave immediately if they could find a comparable job elsewhere.

"People like this city for its economic climate, but it does not have intrinsic appeal," said Frank Newport, a public opinion analyst with the firm of V. Lance Tarrance and Associates.

There is also a growing feeling, voiced more publicly than ever, that the rapid growth of the late 1970s, when Houston was adding more than 1,000 people a week, was bad for the city.

"If some people lose faith in Houston, that's a good thing," one business executive said. "We literally sucked the flotsam of the world down here in the last 10 years. We've got to flush that out of the system."

Others say Houston now lacks the leadership it needs. Whitmire, though still favored to win reelection, has had a string of problems--such as a recent City Council session at which angry police officers crowded into the chambers, forcing her to leave temporarily.

At the same time, the business leaders who once dominated Houston life increasingly have lost both touch and influence. Whitmire proved that two years ago by defeating their candidate, and the transit vote is only the latest example.

One Houstonian who regularly deals with business leaders says many are preoccupied with their own economic problems.

"They haven't lost their can-do attitude yet," he said, "but if economic problems continue, they could."

"Has Houston lost its will to solve its problems?" asked Donald Williams of the Rice Center, which regularly studies the city. "Do we think we can't build that city of the future?

"I don't think that has really changed. Some members of the leadership are less confident than they once were. But there is a younger group of leaders behind them who have not lost confidence. They still feel they can build a city of opportunity and one that gives people freedom of choice."