For more than two years, House Budget Committee Chairman John R. Kasich (R-Ohio) has been the nuclear core of the Republican revolution -- a brash, hyperactive and unpredictable figure.

With his hands on the spending levers, the boyish-looking, headstrong Kasich tried to turn his budget committee into an all-powerful policy directorate for the rest of the House committees. Kasich feuded with the chairmen of the Appropriations and Ways and Means committees, who complained he was overstepping his bounds by dictating policy to them. He was so self-righteous and maniacally energetic that his Ohio colleagues hated to get caught sitting next to him on weekend flights home.

Since the election, Kasich, 44, has tried to soften his image, toning down his rhetoric, mending fences with onetime GOP enemies and stressing the importance of religion and family. Saturday, the once-divorced Kasich married Karen Waldbillig, a hospital communications director from Columbus, Ohio, whom he has dated for eight years.

Kasich says he is striving for a "more even keel" in his lifestyle, but friends and critics alike still see flashes of the old, more combative Kasich. More likely, they say, Kasich has begun to position himself for a presidential bid.

Kasich's name is being mentioned more and more by GOP party officials and operatives in the early speculation about the 2000 presidential race. Already, the eight-term House member has formed a political action committee to help finance his stepped-up speaking engagements as he traverses the country promoting his message of "exporting money, power and influence out of Washington," along with policies that encourage self-help and traditional family virtues.

"I think the single biggest problem we have in the country today is the fact that, because of stagnant wages, it is no longer the choice of a family whether you have one wage-earner in a family," he said. "You've got to have two people working, and this has had the most profound impact on our culture."

The Ohio Republican also is working on a book about average Americans who have led heroic or highly innovative lives (with the working title "Angels on our Shoulders"); co-author Ron Goldfarb predicts it will be the next "Profiles in Courage" -- the prize-winning book that helped launch John F. Kennedy's national political career.

Whether Kasich's political ambitions are too loftily cast may not be clear for some time. What has drawn more immediate concern, at least from those involved, is the impact these developments could have on the upcoming budget negotiations between the White House and Republicans. Among some negotiators, the worry is that Kasich is more preoccupied with drawing the limelight than with finding expedient ways to negotiate compromise.

While many, including House Speaker Newt Gingrich (R-Ga.) and Senate Budget Committee Chairman Pete V. Domenici (R-N.M.), showed considerable flexibility in trying to accommodate President Clinton during the 1995-1996 budget negotiations, for example, Kasich was more stubborn in holding out for GOP principles.

This year, Kasich was the first Republican leader to publicly demand that the president resubmit his balanced budget plan, after a Congressional Budget Office analysis showed it would fall far short of its goal. And while Gingrich voiced optimism last week following a White House meeting with Clinton and Republican and Democratic budget officials, Kasich kept his cards close to the vest.

Kasich, once prone to making rash pronouncements, now says, "You never enter this with any sort of wild expectations of how easy all of this was. When you understand what's going on, you don't go through mood swings. You don't say, Oh, it's great' or Oh, it's terrible.' You really want to maintain an even keel."

White House officials who deal with Kasich regard him as a likable but highly unpredictable antagonist. He can seem amiable and friendly in private discussions, they say, only to display his pique before reporters hours later, impugning not only the bargaining positions but the motives of the Clinton budget team.

"He's sort of the wild card in all of this," said one administration official. "It's hard to read him. It seems like he's capable of jumping in any direction at any time."

Kasich's need to stand out -- to define as sharply as he can differences between himself and the Democrats and between himself and potential rivals within his party -- could pose problems in finding a budget solution this year. He already has riled many GOP colleagues and special-interest groups by pressing for a reduction in "corporate welfare," the government programs and tax benefits targeted to specific businesses and groups.

Kasich won't confirm or deny his presidential ambitions, but he does little to discourage speculation, noting, for instance, that he passed up two opportunities to run for the Senate from Ohio, choosing instead to bide his time for a potentially bigger opportunity. He insists that his long-range political plans will not get in the way of negotiating a budget deal with Clinton, if at all possible.

"First of all . . . I want to get this budget done," Kasich said last week, shortly after returning from a White House meeting with the president and Republican and Democratic budget leaders. "I feel passionately about the fact that the Republican Party has stood for less government and for more power to the people -- which includes tax cuts for people -- and for helping to rescue families in the country."

Rep. David L. Hobson (R-Ohio), a senior member of the House Budget Committee and a close friend of Kasich's, insists that Kasich's mind is principally on the budget, adding that it would be a mistake for him to let his ambitions cloud his judgment.

"Everybody has dreams, and I'm sure John has his," Hobson said. "But if you try to get cute on something like the budget, that's when you get whacked. When you start to believe your press clippings, that's when you get into trouble. John's been around here long enough to know that."

Kasich has spent most of his adult life around politics. He grew up near McKees Rocks, Pa., a blue-collar suburb on the western rim of Pittsburgh. His Croatian grandfather was a steelworker and his father was the town mailman. Although his parents were Democrats, Kasich became a Republican while attending Ohio State University, to protest the "hassles" of the school's bureaucracy. Bold and brash, the young Kasich amazed his schoolmates and friends by wangling a White House invitation to meet President Richard M. Nixon.

During a stint in the Ohio state legislature, Kasich began a tradition of drafting detailed budgets as alternatives to administration proposals. After his election to the U.S. House in 1982, he developed a reputation as a GOP maverick by aligning himself with liberal Democratic Rep. Ronald V. Dellums (Calif.) on the House Armed Services Committee to derail the B-2 bomber program. Later, he teamed up with Rep. Timothy J. Penny (D-Minn.), to promote a number of ambitious deficit reduction plans.

With Gingrich's help, Kasich leapfrogged several more senior Republicans in 1993 to become the ranking member of the House Budget Committee and the sharpest critic of Clinton's early budget and tax policies. When the Republicans won control of Congress in 1994, Kasich was elevated to chairman of the committee and became the chief point man for the GOP drive to balance the budget, dismantle large chunks of the bureaucracy and slash taxes.

Often described as a protege or "kid brother" of Gingrich, who groomed him for a leadership role, Kasich moved out of the speaker's shadows at the height of the 1995-1996 budget war with Clinton. With strong support from the conservative House freshmen, Kasich reined in Gingrich when the speaker appeared to be too eager to cut a deal with the president and end the crisis.

One of the most popular figures on the Republican lecture circuit, Kasich appeared in 38 states for GOP causes last year, and this year has appeared in Georgia, Michigan and Florida.

"Kasich is the most outsider of the insiders and that would make him a serious presidential contender," said Frank Luntz, a GOP pollster. "He's a tremendous speaker, with an aw shucks' style -- the Woody Harrelson of Congress. He's very human in the way he talks, and that makes him very popular."

Luntz added that Kasich's marriage will prove an invaluable asset to his career, describing his wife as a vivacious and winning personality, "the next Jackie Kennedy."

Arianna Huffington, a conservative activist and columnist who has been encouraging Kasich to seek the nomination, said he is a fresh face in a party saddled with tired, "recycled" politicians. "He speaks with a passion," she said last week.

Though he enjoys star status among Republicans, Kasich is wont to spark controversy, as he did recently by agreeing to address a March 31 fund-raiser in Modesto, Calif., for Democratic Rep. Gary A. Condit, one of his closest friends from the opposing camp. California GOP officials griped that Kasich was giving comfort to the enemy.

Kasich also raised eyebrows in GOP circles recently when Nation of Islam Leader Louis Farrakhan repeatedly stood up and applauded a speech Kasich delivered to a conference in Boca Raton, Fla., where he promoted self-help, welfare reform, family values and lower taxes.

Last week, Kasich said he was "shocked" and "surprised" by the attention he received from Farrakhan and had no interest in pursuing a dialogue with him.

"I really don't want to get into a psychological analysis of Louis Farrakhan. It's enough to say, though, that he has communicated some things that are . . . very ugly," Kasich said in reference to what critics have characterized as Farrakhan's antisemitic views. "In order for him to be more effective in being able to communicate with people he needs to heal those very ugly statements."

Kasich now is weighing things more carefully for their longer-term political implications, whether it is a compliment from a controversial black nationalist or the pros and cons of a budget deal.

"Some of it is that I just have a little more perspective," Kasich said. "I've learned in Washington that you not only have to protect yourself against people who say bad things about you, but you also have to protect yourself against people who say good things about you." Staff writer Clay Chandler contributed to this report. CAPTION: Getting ready to seek the GOP nod in 2000? House Budget Committee Chairman John R. Kasich has just gotten married, is writing a book about everyday American heroes and says he is seeking a "more even keel" in his lifestyle.