As she sits behind a big desk in a spacious office in the booming city, Kathy Whitmire -- young, small, female -- seems an unlikely figure for mayor of Houston, Tex.

Houston almost swaggers with affluence, but not the controlled Whitmire. Houston fairly oozes with machismo, but not the feminist Whitmire. Houston gave America urban cowboys. Whitmire dresses for success.

She is in Washington this week for her first visit since a landslide victory last November turned her into the head of America's fifth largest city. It is partially a courtesy trip to call on such fellow Houstonians as Vice President George Bush and White House chief of staff James Baker, and along the way she'll be looking for whatever is left of President Reagan's shrinking federal pie at places like the Department of Transportation and the Department of Housing and Urban Development. But it is also a time when the political and journalistic worlds of Washington will begin to take stock of her, and there may be some shocks on both sides.

The Democratic Party, looking for heroes in the hinterlands, already has adopted her as one of its shining lights. "I'm very pleased with the fact that I hold a nonpartisan position," she says. Esquire magazine has added her to the growing list of neo-liberals in American politics. "I don't know what that means," she says. "You know I like to avoid labels when I can." She will speak tomorrow at the National Press Club, but a week ago, when asked what she would say, responded with a laugh, "When we figure it out, we'll let you know. Hopefully we'll come up with something brilliant."

Kathy Whitmire grew up in Houston believing she would be the wife of a politician. And barely six years ago she was an accountant with a husband trying to get into politics. But in 1976, it all changed for her. Her husband died and she was suddenly, at age 30, at a crossroads. The next year she entered the race for city controller, which she won, and four years later demolished the incumbent mayor, the county sheriff and a flock of lesser candidates to become the city's first woman mayor. Among her most important supporters was the local gay community. "We want to run the city like the big business it is," she said during the campaign.

Now the herd of Houston reporters on her trail and an occasional television network crew wonder what she thinks about the president's budget and his State of the Union speech and the New Federalism, and all she really wants is for everyone to quit badgering her about these things and let her get to work running her own city. "It's a matter of priorities," says the certified public accountant. "I've been barraged with questions . . . and I want to say, 'Look, I've got my own budget to worry about and my city council meets twice a week, don't bother me with this stuff.' "

She is like that about everything, which is why the press is driving her batty after almost 50 days in office. "You know," she says, which is the way she begins most of the sentences that come rolling off her tongue in rapid order, "you know, I have always felt very comfortable dealing with the press."

But when local reporters started following her to the bathroom, her press secretary laid down some rules. No more ambush interviews, no more hounding. In return, Whitmire agreed to meet reporters on a regular basis, but it's obvious the media have become an obsession with her. When she slipped into a pair of blue jeans recently and fled to a suburban mall with a friend to watch her first movie in months, she saw "Absence of Malice." She laughs at herself as she recounts the episode.

"I guess the press does a lot of good, and I'm probably a more productive mayor because of them because they make me do things that I would otherwise put off," she says. Like the morning she woke up during the transition and heard a local radio commentator talking about the upcoming city council meeting, the items that were of interest to Whitmire and the box score the station was keeping on her. "I said, gee, I'm going to get a grade on this, so I spent a whole day lobbying those two issues to make sure I won them, and they weren't that big of a deal until he made them that way," she says.

Whitmire was born on Aug. 15, 1946, and raised on Houston's north side. In those days, Houston was a city without freeways or integration, and Whitmire has watched the economic boom and the civil rights movement transform her home town. Even as a youngster, she showed a desire to chart her own course. Unwilling to walk in the shadow of an older brother, she transferred to a different high school, where she graduated with honors.

Whitmire turned down a scholarship at nearby Rice University in favor of one from Southern Methodist University in Dallas, but returned after a brief stint and enrolled at the University of Houston, where she earned a degree in business administration and a master's in accounting.

She has lived all her life in the city, although she and her late husband Jim, whom she married when she was 20, almost moved to New York City after graduate school. "Then we realized we could buy a house if we stayed in Houston, and that was really the reason we decided to stay," she says. She went on to become a CPA and worked for the accounting firm of Coopers & Lybrand.

She first got the political bug from her father, now 71, an electrical contractor who was active in precinct politics. Her own political career began in the early 1970s, when her husband ran unsuccessfully for city council on two occasions. About this time, she also got involved in women's politics in the Houston area. When her husband lost his eyesight from complications of juvenile diabetes, she left Coopers & Lybrand and set up an accounting firm with him, in part so she could drive him to work. In 1976, her husband died from the disease, and it was then that friends urged her to enter politics on her own, something she had been thinking about for some time. "I was really at a turning point about what I was going to do now that I was single again and kind of at a starting-over point."

She jumped into the controller's race when incumbent Leonel J. Castillo quit to become head of the Immigration and Naturalization Service in Washington, and her entry turned the lackluster campaign into a rallying point for women's rights in Houston. As with the mayor's race last fall, she led in the first round of voting and won in a runoff. In two terms as city controller, she earned a reputation as a bright, skillful manager and unyielding critic of Mayor Jim McConn's two-term tenure as chief executive, once ridiculing a $1 million street inventory he had proposed as "a pothole study."

In last year's mayoral election, she led a crowded field in the first round of voting, in which McConn finished a distant third, and then, as smart money began to flow into her once low-budget campaign, devastated Harris County Sheriff Jack Heard in the runoff, garnering 62 percent of the vote.

Today she appears totally immersed in her job, with little time left for other interests. She shares a duplex with her brother and sister-in-law in the Montrose section of Houston, a close-in neighborhood akin to Washington's Dupont Circle or Adams Morgan. During the campaign, she would come back to the house late at night with a carton of yogurt and some grapefruit juice and watch herself on the video recorder her brother and sister-in-law used to keep a record of her television appearances. She has no political heroes and few hobbies, except a love of food and swimming in her own pool. She follows the news religiously and for light reading enjoys a budget or reports on government and politics. Although she sees a number of men socially, there is no particular man in her life. She has no children from her earlier marriage.

She is an easy talker, but there is nothing frivolous or flamboyant about her. She has a bit of Jimmy Carter in her, a manager's desire to control things, a penchant for believing the road to political heaven is through a reformed civil service and a certain pride in her stinginess. She ran on the theme of providing more services with no more money, and proudly calls herself, when she is forced into the label business, a fiscal conservative and a social progressive. "I guess that's neo-something," she jokes.

"You know, I am wondering at this point which party is ultimately going to identify itself more with that combination. I don't know. I don't see either party doing it right now. You saw all the things that happened in the Republican Party during Ronald Reagan's election -- opposition to equal rights, anti-abortion, just really a lack of sensitivity which really depressed me and a lot of my Republican friends. At the same time, every time I hear representatives of the Democratic Party getting up and lambasting everything that the administration in Washington tries to do toward fiscal responsibility, you know that doesn't give me much hope for the Democratic Party at the national level either."

Whitmire will necessarily avoid the national limelight, for she has problems to solve at home. For years, a network of good old boys controlled the city and its weak-kneed government, but in the last decade the character of the whole place has changed, with 45 percent of the population having arrived since 1970. Whitmire is cut from the mold of this new Houston, which has more style than its older cousin, which worries less about stature and more about results. It was this new, evolving Houston that elected her last fall, and to which she recognizes her allegiance.

"My objective," she says, "is to do a good job of managing this city and setting it in good stead for its future, and that doesn't really require me to get involved in state and national politics and take sides . . . I take pains to make sure I don't make my Republican constituents feel disenfranchised and that I don't alienate the Republican administration in Washington. I find it disadvantageous to be partisan."