On the set of NBC's "Meet the Press," House Budget Committee Chairman John R. Kasich (R-Ohio) had just launched into an animated description of Republican plans to "slow the growth" of Medicare and Medicaid spending.

Sitting next to him, Laura D'Andrea Tyson, President Clinton's national economic adviser, listened politely -- until she just couldn't take it anymore.

"Excuse me?" she broke in acidly. "Can I say something? . . . Let's be serious here."

Within seconds, the staid Sunday talk show erupted into a shouting match. Kasich blasted the White House for tolerating runaway federal budget deficits. Tyson denounced Republicans for gutting programs for the elderly and the poor.

"Laura, I'm sorry -- those numbers are wrong," Kasich fumed.

No, your numbers are wrong, Tyson shot back. "You know what?" she added, turning to moderator Tim Russert. "You should have on this program someone to do fact-checking."

It was the sort of strident confrontation Tyson said she would have had trouble imagining during her days as an economist on the mellow University of California at Berkeley campus. But increasingly, Tyson -- who came to Washington two years ago with virtually no political experience -- has emerged as one of the Clinton administration's most combative defenders of the president's economic policies.

It isn't that she has become more partisan, Tyson insisted in a recent interview in her cramped quarters on the second floor of the White House's West Wing. Rather, she said, the sort of rhetorical posturing that often passes for serious debate in Washington has stretched her patience.

"I have a very low tolerance for statements that are factually or analytically incorrect," Tyson said. "I come from a world where things like accuracy and the truth of what you say are very important." When confronted with arguments she finds deceptive or misleading, Tyson said, "I tend to respond with . . . determination."

There's a hard edge to the woman Clinton picked earlier this year to replace soft-spoken financier Robert E. Rubin as head the National Economic Council. In her new job, though, she has had to swap her economist's sense of certitude for a politician's pragmatism.

In her previous post as chairman of the president's Council of Economic Advisers, Tyson was free to speak her mind. As guardian of the administration's credibility on economic matters, she seemed to relish prodding colleagues to abandon politically appealing notions that might prove vulnerable to attack on economic grounds. As the administration's leading spokesman on economic matters, she learned to choose her public comments carefully as she defended such policies as health care reform and threats of retaliation against Japan over trade -- even though she had argued vehemently against them in debates with her White House colleagues.

Tyson still has strong opinions, but in her new assignment she has had to play the role of "honest broker," working to ensure that other members of Clinton's economic team get their say.

The transition hasn't been easy, she acknowledged. "I started as an academic economist, so maybe more than Bob I have quite strong views on the economic issues myself," she said. "I try to make sure . . . my own views don't distort the process. . . . It's part of the challenge of the job for me."

"On the outside, she's become more of a fighter," said Gene Sperling, Tyson's deputy for domestic policy. "But on the inside, she's become more of a conciliator." Tyson vs. Rubin Many colleagues describe Tyson's management style as a departure -- some say a welcome one -- from Rubin's unobtrusive manner. "Laura is a closer,' " observed one member of the Clinton Cabinet. "Bob was very effective, but he was so low-key you weren't really aware of him steering a meeting. . . . With Laura, there's a little less deferring to others." At the conclusion of a discussion "you get a clear summary of where things stand."

Tyson and Rubin, who is now treasury secretary, developed a friendship in the early days of the administration and remain close; she talks with him by telephone daily, consults with him more frequently than any other member of Clinton's inner circle. But Tyson is quick to point out that she and her predecessor have very different styles. "I'm not Bob," she declared firmly, minutes after ending a phone conversation with the treasury secretary last week. "We are very different people."

On a table along the back wall of her office, Tyson keeps a favorite photo that shows her and Rubin speaking to reporters in the White House briefing room. As Rubin speaks, Tyson -- chewing on the cap of her pen -- fixes him with a look of deep skepticism.

"That is a classic look of mine at him," she said with a laugh. "It's like, Am I going to let this guy get away with this?' "

These days, Tyson stands at the center of the decision-making process on two of the administration's most visible policy fights -- the battle with Congress over the budget and the battle with Japan over trade.

At the behest of White House Chief of Staff Leon E. Panetta, she has taken charge of coordinating the administration's attack on congressional Republicans' budget proposals. Each Monday and Thursday afternoon, she runs an hour-long meeting of about 15 top administration officials, including Rubin, Panetta, Office of Management and Budget Director Alice M. Rivlin, the heads of the key economic agencies and key political advisers. They gather in the West Wing's Roosevelt Room to swap intelligence about Republican budget policies, debate which measures the administration will or won't accept and fine-tune the White House's effort to communicate its views.

Tyson also presides over the meetings at which top Clinton advisers plot the administration's aggressive approach to trade negotiations with Japan on autos and parts. Unless Japan's carmakers abandon their staunch refusal to renew annual purchasing targets for U.S. auto parts by mid-June, the group must consider whether Clinton should follow through with his threats to slap sanctions on Japanese-made luxury cars.

Tyson initially had resisted administration officials' pleadings that she trade her job as Clinton's chief economist for the more powerful directorship of the NEC -- in part because she had seen how heavily the responsibility had weighed on Rubin. "He was always on the run, he practically lived here and worked until very late in the evening," she said.

Now it is Tyson's turn to spend weekends in the office and field late-night phone calls from Sperling and his cadre of nocturnal budget wonks. Since taking the job, she said, her life has been "stress, long hours, travel and unpredictability. In any given day, you go in at 7:30 in the morning and what you thought your day or your week was going to be like can change in the course of a half-hour discussion."

The new job also has brought greater access to the president. She has three regular meetings with Clinton each week; as CEA chairman, she had only one.

And it means her public comments are dissected with an intensity to which she is not accustomed. She was surprised earlier this month by reaction to her comments that balancing the budget risked slowing economic growth and might even tilt the economy into a recession. Tyson often expressed that concern while CEA chairman, stating it formally in the latest Economic Report of the President.

Some reporters, however, interpreted Tyson's statement as a evidence of a shift in the administration's position on the value of deficit reduction. The comment was taken "much more politically than if I had said the same thing as the CEA chair," Tyson said. Now that she is the president's national economic adviser, she marveled, "people seem to respond to me in a different way." Advantages From Academe Tyson's role at the CEA fit neatly with her academic background. There, she commanded a team of highly trained professional economists and had access to a wealth of government economic data. But at the NEC -- which Clinton had promised in his campaign to establish as the economic equivalent of the National Security Council -- she has a smaller staff and must rely on numbers crunched by other agencies.

"In my old job, I looked at all kinds of numbers, but in my new job I can barely find them," Tyson lamented at a recent luncheon with Washington Post reporters and editors.

Thomas P. O'Donnell, Tyson's chief of staff at both the CEA and NEC, fought an unsuccessful battle to persuade Tyson to leave her computer terminal at the CEA, hoping to keep her from getting too bogged down in the details of the different policy recommendations that cross her desk.

"By nature, Laura tends to get more absorbed in the substance than Bob," said one of Tyson's White House colleagues.

But Tyson pays attention to the nuts and bolts of management, as well. In an effort to enhance the value of the budget strategy sessions, she has limited attendance to major players, thinning the ranks of aides and assistants that used to fill the chairs along the Roosevelt Room's back wall.

Tyson takes pains to keep the meetings focused on politics as well as policy, encouraging Clinton's political advisers to participate. "The world has changed" since the Republicans took control of Congress, said White House lobbyist Patrick Griffin. "Laura has recognized that and tried to keep the process relevant."

The sessions have become a vital "clearinghouse" where "strategy and tactics weave together," said senior Clinton adviser George Stephanopoulos.

In those meetings, Tyson said, she is shedding her economist's air of certainty. "It is important if you are going to bring economic perspective to a discussion that you not do it as if you have a total monopoly over the truth," she said. To do otherwise "puts people off. . . . You just turn people away."

But outside the White House, Tyson sometimes has trouble containing her conviction that she really does know best. During a House Budget Committee hearing in February, for example, Tyson angrily refused to answer a question from freshman Rep. Steve Largent (R-Okla.) because he had disparaged Tyson's written statement.

"Either I'm ignorant or this is so totally disingenuous, it is hard for me to even read this," said Largent, a former professional football player with the Seattle Seahawks. " . . . Some of us may like what you say and some of us may not . . . but the bottom line is it doesn't matter because we can pull in just as many economists that can say the opposite."

Tyson was incensed, and declared she saw no need to answer Largent's query "because you have already stated that you are not going to believe anything I say."

She eventually gave her answer -- after extracting an apology from Largent. But she couldn't resist taking a swipe at her interrogator: "I did not say to anyone on the committee they were disingenuous or hypocritical," she said. "To the extent that I have those views, I restrain myself from making them in a public statement." Recalling the exchange, Tyson said she was surprised by the intensity of her response. "It was like, Where did that come from?' " she said with a laugh. "I was so annoyed that my whole profession was being dismissed by someone who had absolutely no basis for doing that," she said. " . . . I feel I see the problems so clearly, and that is very energizing." CAPTION: Tyson keeps this photo of herself and predecessor Robert E. Rubin, now treasury secretary, in her office. "That is a classic look of mine at him. It's like, Am I going to let this guy get away with this?' " CAPTION: Laura D'Andrea Tyson in her White House office: "I have a very low tolerance for statements that are factually or analytically incorrect."