Twice a day, Thomas M. Downs slips into the spacious, high-ceilinged office of D.C. City Administrator Elijah B. Rogers for some tutoring on how to run Washington.

"I push him. I lean on him," Rogers said. "He says I beat up on him."

Rogers said the grueling initiation is mandated by the intense pressure and political sensitivity of the city administrator's post, which Downs will assume in two weeks--a job Rogers says is "like sitting on a time bomb. You just don't know when it's going to go off."

As the city's top nonelected official, Downs will be Mayor Marion Barry's chief lieutenant, responsible for forcing the city's $2 billion-a-year bureaucracy of 30,000 employes to respond to the mayor's orders and deliver basic services, such as garbage collection and police and fire protection, to Washington residents. Rogers is leaving May 27 to take a job with a private accounting firm here.

Downs, 40, a Midwesterner who joined D.C. government less than three years ago as Barry's director of transportation, has catapulted to the top of the city's bureaucracy on the strength of his reputation as a nimble, expert administrator.

In a government that has a reputation for not working, Downs stood out as a manager who could get things done. He is credited with making the Department of Transportation one of the city's best-run agencies.

Now, as he faces the biggest challenge of his career, Downs will be forced to show whether he has the political acumen to win Barry's confidence and survive in a highly competitive, aggressive, close-knit administration

Until Rogers arrived on the scene four years ago, the dominant figure under Barry was his longtime political adviser and friend, Ivanhoe Donaldson, an aggressive behind-the-scenes operative who is fiercely loyal to the mayor.

But Rogers, with his own aggressive style, won Barry's trust and became an independent force in the administration. As a result, he came to exercise sweeping powers over the government's daily operations, and is credited with implementing professional management techniques that have improved the city's much-maligned bureaucracy.

"Whatever you want to say about Elijah Rogers, he made decisions and stuck to his guns," said one former Barry administration official who asked not to be named. "He didn't let Ivanhoe Donaldson walk over him at all."

Present and former Barry aides wonder whether Downs, who has a diplomatic, easygoing style, is tough enough to play the political hardball that is a hallmark of the Barry administration.

"[Downs]is not as tough as I'd like him to be on some things," Rogers said. "I think at times Tom tries to please too much. I stay on him about that. He's gotten tougher in the last year."

Barry said the city administrator's job by its very nature will toughen Downs. "Bureaucrats have a way of getting around you unless you watch them," Barry said. "He's a quick study. You can't intimidate him."

Downs, a slight man who served as an infantry officer in Vietnam, said the questions about his toughness come from people who mistake his low-key, friendly style for softness. "A good manager brings with him a tool bag of skills," Downs said. "Being hard is a skill, but it's just one."

Downs and Rogers cut sharply different styles.

Downs likes to work in his shirt sleeves and wears modest suits. The fast-talking Rogers wears well-tailored suits and never rolls up the sleeves of his shirts, which are embroidered with his middle name, Baby. Downs is casual and open with his staff. Rogers is a stern, demanding boss.

Downs owns a 1977 Pontiac, but usually rides the Metro to work. Rogers pulls up at the District Building in a 1983 Porsche.

Despite the surface differences, though, the men are old friends, and there is a camaraderie between them from the years both have spent as professional administrators. They met through the International City Managers Association in the early 1970s. "Tom and I go way back," Rogers said. "We're close professionally and we like each other."

Rogers recommended Downs to Barry, who hired him as transportation chief in January 1981.

Transportation workers, community activists and business leaders praise Downs' effectiveness. They also say they like his unpretentious, outgoing personality and his wry sense of humor, which is capped off with a disarmingly hearty laugh.

"You ever hear his laugh, God, it's contagious," Rogers said.

"We're very up on Tom Downs," said John R. Tydings, executive director of the Greater Washington Board of Trade, the city's major business lobby. "If we didn't always agree with his final decision, we always felt he had a willingness to hear us."

Downs started his career in Little Rock, Ark., where he worked in the city manager's office for five years and rose to the rank of assistant city manager. He then served for three years as city manager of Leavenworth, Kan.

"It didn't take him long to decide what the community wanted," said John F. Denney, who was Leavenworth's mayor during most of Downs' stay and said Downs did an outstanding job. "When he went to Washington, I told some of my friends we wouldn't see him back out here."

Downs came to Washington in 1978 by winning a highly competitive White House fellowship that landed him a job in the Carter administration as a special assistant to Brock Adams, then secretary of the U.S. Department of Transportation.

"I didn't know anything about transportation," Downs recalled, but "I decided that if I was going with the feds I ought to learn something new and potentially useful in the urban environment."

Downs stayed in the transportation department after his one-year fellowship ended, working as an administrator in the Federal Highway Administration and the Urban Mass Transportation Administration.

But cities remained his first love. At the Department of Transportation, Downs said, officials once followed his recommendation on how to spend $300 million in federal funds. "It was probably the largest single investment I influenced," he said, but the money went into programs that he never saw first-hand. "I know the programs were funded," he said, "but I couldn't get a personal connection to it."

When the Carter administration went out of office, Rogers introduced him to Barry, and he returned to local government.

Last January, as Barry entered his second term and launched a reorganization of the government, he gave Downs added responsibilities as the city's public works director. Downs has been overseeing the merger of three major city departments--transportation, environmental services and general services--into a single agency.

Downs also will have the title of deputy mayor for operations. Unlike Rogers, who had sweeping powers over all city agencies, Downs will share duties with Donaldson, the deputy mayor for economic development, and Alphonse G. Hill, the deputy mayor for financial management. The three deputy mayor positions were created under Barry's reorganization.

As a result, though Barry says Downs' new job is as "first among equals," the post is expected to take on more technical overtones, consistent with Downs' experience as a professional administrator.

Hill, a respected financial analyst who was recruited from a Chicago accounting firm and was city controller in the first administration, is in charge of the city's troubled finances and budget.

Donaldson, who managed both of Barry's campaigns for mayor, officially oversees the city's extensive housing and redevelopment program, including major real estate deals, planning and business development. But his influence extends to virtually all aspects of the D.C. government--recently, for example, he played a role in the mayor's efforts to persuade the lottery board to reverse its decision on a major contract.

How Downs gets along with Donaldson will in a large way determine the degree of independence and power Downs will have, said past and present members of the administration.

Donaldson downplays his importance and says that he plans to leave the government soon. "There are new players coming on the scene. Tom is going to be a principal player," Donaldson said. "He's very astute. He gets things done."

Downs said that he and Donaldson have good rapport, and will have no problems working together. "I respect him immensely," Downs said.

Another possible concern for Downs is that he is white in a city whose population is 70 percent black and in an administration that is black-controlled. "It's a factor for someone who is white, just as it would be a factor for a black being a partner in an all-white law firm or being vice president of IBM," said a former Barry administration official.

Barry said race was not involved in his selection of Downs."There probably will be some in the community who look at this as a question of race," Barry said. "They shouldn't do that."

"Nobody has ever treated me in this government as if I was a minority," Downs said.

Downs took over the transportation department from Douglas N. Schneider Jr., a dedicated advocate of mass transit. Department employes said Downs continued the commitment to mass transit, but also moved in other areas, among them repair of streets and bridges, and motor vehicle services such as car registration.

Downs said his decision to become a local government administrator was in part influenced by author Jane Jacobs' 1961 book "The Death and Life of Great American Cities," which blasted urban renewal programs for destroying the vital fabric of urban neighborhoods. He said the book made it clear that "cities lived and died at smaller unit levels because that's where everyone lived."

Downs grew up in the heart of Kansas City, Mo., in a downtown neighborhood that has now been eliminated by urban renewal.

The oldest of three children in an Irish family, he attended Catholic schools through college and graduated in 1964 with a degree in English from Rockhurst College, a small Jesuit school in Kansas City. He later received masters degrees in political science and public administration.

He lives with his wife, Frances Lorrene, and his 13-year-old son, Luke, in the same Upper Northwest house he bought when he moved to Washington in 1978.

Downs said he is ready for the city administrator's job and is eager to help lead "the city that has won my heart and my family's heart more than any one we've called home."

"It's what I've spent most of my life learning to do," he said. "This is where I want to ply my trade. And for this mayor."