Holding on to Houston

Riding out a hurricane, or riding herd on the indomitable spirit of this city , Mayor Kathy Whitmire wants to keep the reins of Houston in her hands. Mrs. Whitmire, who wrested control from an 'ole boy' network two years ago on a platform of fiscal reform, announced her bid for reelection Thursday.

Polls show her well ahead of her only announced opponent - Bill Wright, a former Whitmire supporter - but Mrs. Whitmire faces some considerably tougher issues than she did in her first mayoral election.

Houston just isn't operating like the maverick city it was when Mrs. Whitmire was ushered into office by a coalition of minority and young professional voters at the peak of the Sunbelt boom. And the mayor, faced with the need to provide government services to a city with a tradition of little government control or taxation, now is helping Houston to deal with what the rest of the nation has been feeling for several years - a fiscal crunch.

Hurricane Alicia, which racked this city Aug. 18, has posed considerable city management problems. But it has been viewed as a political opportunity for the mayor, in that she can showcase her leadership abilities, and it is a possible alibi for a poor system of city services.

The economic slump, only recently showing up in unemployment (10 percent) and business statistics here, has led to a $30 million shortfall in expected sales-tax revenues.

Unwieldy city service agencies - known, for example, for slow trash collection and poor road maintenance - which Mayor Whitmire upgraded with innovative management programs, now face cutbacks.

Though ostentatious sprawl is still noticeable amid Houston's unzoned urban explosion, the ripples of the recession have muffled the bluster of Houston's growth and prosperity. The economy here has been battered by the oil glut, which has significantly flattened business in the area. (Port activity, for example, is down about 50 percent.)

The 360-degree skyline of skyscrapers and apartment buildings is the most obvious outward sign of Houston's uncontrolled growth. Here, too, may be the most obvious signs of a slump, as developers complete giant skyscrapers that have no prospective occupants to fill them. Many apartments, at a premium during the peak of the Sunbelt migration, now sit empty, and developers even offer months of free rent and prizes to entice renters.

Political observers say Mrs. Whitmire's management can't be blamed for the current economic slump here. But they say the mayor of the nation's fourth largest city will be called on during the campaign for the November election to suggest ways to help the city face limits that it never had to respect before.

The business slump, she explains, really didn't cause the city any loss of sales-tax revenues. Revenues for fiscal year 1982-83 were $140 million - not down from the previous year, but $30 million less than the expected increasem in sales taxes, she says.

Vowing ''to keep Houston out of the cycle of higher taxes'' that will drive business away, she proposes belt-tightening and the postponement of equipment purchases. A long-term solution she mentions is to attract a more diversified economic base that is less dependent on the oil industry.

Mrs. Whitmire has been criticized largely for not being an effective leader or political team-player. She's had a spotty record in gaining a coalition of power on the city council; angered members of the police department to the point that they rioted at a City Council meeting; and was unable to rally community support for a large-scale mass-transit system that many say is badly needed.

Nevertheless, she has made some politically popular moves. Most notably, she recruited Atlanta's Lee Brown to be police chief. He is the city's first black police chief, in a department long-troubled with racial problems. She also has attempted to revamp the civil service here to get more responsive department heads. One successful part of this effort included getting private industry to ''loan'' their executives to the city, to increase City Hall efficiency.