She is spending $13 million a day and has come perilously close to running out of money, but that's not her biggest worry. Census Bureau Director Barbara Everitt Bryant has a platterful of problems.

She is faced with angry city officials and skeptical members of Congress, critical of the 1990 census just as it hits its peak operation this spring. She has been dogged by an unexpectedly anemic public response to the census, a mail-back rate so low it will cost the bureau an extra $70 million. She is finding a serious shortage of census-takers in some parts of the country.

And over the next year, she will be center ring in undoubtedly the most bitter fight of the 1990 census -- whether population totals should be "adjusted" statistically to compensate for counting errors, a decision worth millions of dollars and considerable political power to some communities.

And while Bryant's most immediate financial problems were solved when Congress appropriated $110 million in supplemental funds last week, the other problems are not so easily dispatched.

It has been just under six months since Bryant took over as director of the nation's largest peacetime special operation, the $2.6 billion national head count that comes only once a decade.

"I knew it would be a hot seat," she said. Her friends, she added, advised her to take the job only if she could take the heat. "I thought I could, obviously."

Bryant, who swims a half-mile every morning and commutes long-distance to see her husband most weekends, minimizes the problems she faces, maintaining that this is "the best-planned census in history."

And when she discusses the challenges before her, she does so matter-of-factly, but with a slight, steady smile parting her lips, as if she had just entered a cocktail party. It is a curious and disarming combination, one that has helped her through combative congressional hearings and boisterous news conferences.

Perhaps because of what many say is an imperturbably graceful manner, she is spoken of with the kind of deference reserved for the clergy, even among partisan opponents:

"Bryant is a very charming person," said Jeffrey M. Wice, an attorney representing New York Democratic leaders on redistricting issues that have pitted him against the administration.

He tells of seeing Bryant at a state legislators conference in Idaho and, although the two had never been introduced, Bryant turned to him and said, "I know you're from New York and we're going to take care of you, don't worry."

"She seems to be a very nice person and she's trying her best, but the die was cast before she came in," said Rep. Charles E. Schumer (D-N.Y.), one of the members of Congress who has been most critical of the census, claiming that outdated methods will cause a serious undercount. "It's sort of a thankless job."

Colleagues and observers say Bryant, 64, will ultimately be judged not only by the success of the 1990 census but by her willingness and ability to protect the Census Bureau from what many say is an increasing threat of political interference, particularly from the Commerce Department, the bureau's parent agency.

While no one is accusing the bureau of manipulating data or other blatantly improper activity, Schumer and other Democrats charge that policy decisions -- primarily whether to adjust the census -- are being made by Commerce officials on partisan, rather than technical, grounds. The belief is that the Commerce Department is prejudiced against adjusting the 1990 census because adjustment would benefit the Democratic Party, whose constituents are most likely to be undercounted.

"The ultimate question in terms of Barbara and how she does is how she does with her bosses," said Kimball Brace, president of Election Data Services, a political consulting firm that specializes in redistricting. "It's become a more politicized bureau. . . . Is she going to be able to bring back a non-political bureau, as it used to be?"

Commerce Undersecretary Michael Darby denies that the department is interfering in bureau affairs. "I just don't see that as a serious problem," he said. "It's more an advocacy charge than a reality."

Bryant also dismisses those who say her role will be to protect her agency from outside meddling: "I don't feel the bureau is politicized at all."

Bryant was appointed in December 1989 only after it became clear that some congressional Democrats would fight the administration's first choice, Alan Heslop, a California academic who had been heavily involved in redistricting.

She had worked nearly two decades in executive positions at Market Opinion Research, a major Republican polling firm in Michigan where Robert M. Teeter, a close adviser to President Bush, formerly served as president. But she was not politically active, and in the wake of the stymied Heslop confirmation, she appeared comparatively nonpartisan.

Her interest in survey research stemmed from a longtime fascination with science. She said her father, who was dean of engineering at the University of Illinois, passed on to her his interest in science and math. And he taught her the importance of speaking before a crowd with confidence and humor.

Bryant said when she was preparing her speech as high school valedictorian, her father told her, " 'If you can't make the audience laugh, I'm not even coming.' "

She went on to study physics as an undergraduate at Cornell University, married John H. Bryant, an electrical engineer, and raised three children. She began graduate school when her youngest child was in elementary school.

She received a master's degree in journalism and a doctorate in communications, both from Michigan State University, where her studies included "a heavy dose of survey research," she said. It was that interest that led her to Market Opinion Research.

Now Bryant, the first woman to run the bureau, spends her weeks traveling the country promoting the census and in meetings with her senior staff, stopping at grocery salad bars to get her dinner. Her husband has remained in the couple's Ann Arbor home, and Bryant lives in a Washington town house, but the two get together most weekends.

She can handle the stress of the job, she said, "because I keep some decent balance between my work life, getting exercise, having some fun, and I have a tremendously supportive family."

Bryant's future at her post, for which she receives an annual salary of $78,200, is in some question because her appointment -- made during a congressional recess without a confirmation hearing -- will expire with the congressional term late this year. Congressional staff members said confirmation hearings may still be held this summer.

In the meantime, she will undoubtedly face numerous hitches, overseeing her work force of more than 300,000 and the complicated logistics of releasing mountains of politically volatile data.

"Barbara Bryant stepped into a very difficult situation quite late in the game," said Rep. Thomas C. Sawyer (D-Ohio), who chairs the House Post Office and Civil Service subcommittee on census and population. While Sawyer said he is confident in Bryant's skills and commitment, he added: "Does that mean I think the job is doable? That lies before us."