Every twenty-five years or so since 1914, New York's Democratic establishment has been routed by a Republican reformer leading a rickety coalition of business elites, patrician good-government types, burghers, newer immigrants and other groups on the outs with the machine. By that standard, Rudolph Giuliani, the city's 107th mayor, is a typical successor to John Purroy Mitchell, Fiorello LaGuardia and John Lindsay. But while Giuliani's Republican predecessors moved leftward in office to offset conservative dissatisfaction, he isn't following them. Where LaGuardia and Lindsay championed the welfare state, Giuliani is dismantling it. His fiscal conservatism, his distant relations with blacks and his sermonettes on personal responsibility reinforce his sometime image as a right-winger.

Then again, Giuliani was disowned during last fall's campaign by conservatives William Bennett and Patrick Buchanan, who said he was "too liberal" for the gop. And he was embraced by such Democrats as the late Robert Wagner Jr. and actor Ron Silver, who argued that Giuliani was a pragmatist responding to upheavals that are transforming America's cities. Even black Democratic mayors such as Detroit's Dennis Archer and Cleveland's Michael White are saying and doing virtually the same things Giuliani is.

So which is it: Is Rudy Giuliani a New Democrat or an Old Republican? The truth is, he's a hybrid we'll see more of in the '90s--a mayor who subordinates partisanship to "reinventing" municipal government and reviving urban investment. Part of this message comes straight from Bill Clinton's campaign playbook: transcend racial grievances, boost the economy and education and get tough on crime. But unlike Clinton, Giuliani and his counterparts aren't beholden to traditional Democratic constituencies like unions and civil rights groups. Unlike Ronald Reagan, who preached fiscal and personal discipline while pushing an anti-urban agenda, they stake their careers on improving public safety and public schools.

Also unlike Reagan, Giuliani's conservative tone is softened by liberal grace notes, such as support for gay rights and a bill to keep protesters from blocking entrances to abortion clinics. And liberals often find they like Giuliani when they meet him in person. Unimposing in boxy suits and nerdy glasses, he wields a self-deprecating wit and a lawyerly erudition.

Ultimately, however, Giuliani will be judged by what he does, particularly in three areas: the budget, race and political style.

Budget. Giuliani faces a $2.3 billion deficit in the city's $31 billion budget, rising unemployment and a welfare caseload of 1.2 million people--more than one in seven New Yorkers. His response has been starkly conservative: cut taxes on hotel and commercial occupancy to encourage economic revival and shed 15,000 of the city's 214,000 workers through a severance plan wrested from municipal unions. Next month, Giuliani will begin to push an austerity budget—his equivalent of Reagan's Omnibus Reconciliation Act of 1981—through New York's restive City Council.

Especially controversial is Giuliani's insistence on exempting cops, firefighters and teachers—who are mostly white—from any cuts. That puts an unbearable strain on other agencies struggling with poverty, aids and child abuse. Giuliani insists that improving safety, schools and jobs, even at the cost of painful dislocations elsewhere, will benefit the poor more than anything that social service bureaucrats and racial activists have done. (It will also benefit the police and fire unions, which supported him last fall, and the teachers' union, which abandoned his predecessor, David Dinkins, and remained pointedly neutral.) Such selective retrenchment enrages the left. "There is something unseemly about preaching the value of work while cutting back jobs, opportunities and hope," David Jones of the Community Service Society wrote recently in Harlem's Amsterdam News. The mayor's reply—that no community can thrive when tax-draining public jobs drive out tax-paying private ones—seems a cold abstraction to his critics.

Looking past the July 1 budget deadline, Giuliani has advisers working to bring future budgets into balance. He plans agency consolidations and eliminations; managed competition and partnerships with private contractors; sales of city assets, including two municipal hospitals; and new procurement and hiring policies. He is also demanding unprecedented influence over independent public authorities, complaining that they misspend billions in city tax dollars. For example, he is withholding funds from the Metropolitan Transportation Authority, which opposes his plans to merge its police department with the city's. "If the mta wants its own police force, let them pay for it," he snaps. "Why should I write a $300 million check when they have salaries and perks I couldn't tolerate?"

In a late-night confrontation two weeks ago that prompted schools chancellor Ramon Cortines to resign, Giuliani won 2,500 administrative cuts from the semi-independent Board of Education, to which City Hall gives more than $3 billion per year. And he appointed a political ally, Herman Badillo, as a mayoral counsel to oversee school finances. Only Governor Mario Cuomo's intervention persuaded Cortines to stay on the job. Undaunted, Giuliani is now wrestling with the powers in Albany in pursuit of state aid.

Race. Last fall, after Giuliani carried less than 5 percent of the black vote in defeating Dinkins, some black politicians publicly warned other blacks not to shake hands with him--let alone work for him. Yet Giuliani has hired half a dozen black commissioners, and in a recent Daily News poll, 21 percent of blacks rated him favorably.

Giuliani's layoffs and service reductions will hit blacks hard because they depend heavily on the public sector. Equally problematic is his laudable effort to shift the city's racial discourse to a "single standard" of debate. A premise of his campaign was that many people of color reject race-based educational and economic remedies. Like his counterparts in other cities, he did well among Asian American and Hispanic voters. That blunted charges of racism, but not blacks' fears of losing ground.

For example, predictions that Giuliani's cops would declare "open season" on blacks seemed justified when, a few days into his mayoralty, police in Harlem answered a phony robbery call and stormed a Nation of Islam mosque. Giuliani coolly sidelined Al Sharpton's "mediation" efforts, however, and his insistence on treating the incident as a police matter was vindicated as it became clear that cops had been beaten by enraged worshipers, not vice-versa. "I don't have a special message for any group," Giuliani says. "People in this city don't need special things. They need more of certain general things—safety, education, jobs. The officers who went into that mosque didn't ask the color or gender of the people they were trying to protect. That's how most New Yorkers conduct themselves, and it's how I'll run this administration."

After the tortuous racial etiquette of Dinkins's "gorgeous mosaic," such preaching sounds almost otherworldly, and many blacks feel that it masks racial double standards. Giuliani won the endorsement of Ruben Franco, director of the Puerto Rican Legal Defense Fund, by lobbying for an odious redistricting scheme that produced the convoluted "Hispanic" twelfth congressional district. Franco now chairs the New York City Housing Authority. Giuliani also awarded a cushy advisory post to Dinkins's fire commissioner, Carlos Rivera, who broke ranks and endorsed him toward the end of the campaign. Loyalty to supporters is nothing new, but in Giuliani's New York it deepens blacks' isolation.

In January Giuliani came out against price preferences for minority bidders on city contracts, which he says pervert affirmative action and sometimes reward "fronts" for out-of-town whites. Blaming such contracts and patronage for massive cost overruns in the $1 billion reconstruction of Kings County Hospital, which serves poor blacks, he slapped a moratorium on the project. In February he proposed that the city start "finger-imaging" welfare recipients to prevent fraud and that the data be accessible to law enforcement agencies. City Councilwoman Una Thomlinson-Clarke likened it to "branding the slaves" until it became clear that many city employees, including all commissioners, already submit to it.

Giuliani needs to show he is color-blind on corruption. He recently oversaw the arrests of fourteen cops for drug-related corruption and brutality and made them do on-camera "perp walks" in handcuffs. That helps.

Style. Every day at 8 a.m. Giuliani huddles with a dozen top aides, including assistants from his days as U.S. attorney as well as his oldest friend and alter ego, Deputy Mayor Peter Powers. They function like a group of white men who have played hockey together for years; newcomers such as Deputy Mayors Ninfa Segarra and Fran Reiter are still feeling their way. Still, half of the mayor's outer circle of commissioners and senior aides are women and minorities.

Yet Giuliani's style leaves a lot to be desired. He's prosecutorial: he often impugns the motives of colleagues in government who question his priorities. "It's intended to make them feel some pain for what they're doing," Giuliani told me. What they're doing, he thinks, is avoiding the tough decisions that face a mayor, who alone must reconcile fiscal and political pressures.

That doesn't explain why Giuliani snubbed Clinton in March by skipping his town meeting on crime at Brooklyn College. The mayor, who as a former U.S. associate attorney general qualifies as an expert on crime fighting, considers the president's crime bill a fraud. Still, Clinton was furious—"No other mayor in America has refused to see me," he told an associate—so Giuliani, blaming a miscommunication, rushed to meet Clinton at his hotel later that day. There, he says blithely, he impressed upon Clinton the importance of his own crime-fighting initiatives.

Yet Giuliani has been noticed in Washington for adopting a transpartisan pose. At a recent crime forum his pragmatic observations from the urban trenches were seconded more often by Democratic Senator Joseph Biden and Representative Craig Washington than by gop Senator Phil Gramm. At a Washington Times editorial board meeting, Giuliani refused to pile on Whitewater or to endorse privatizing New York's public schools.

What does all this say about Giuliani's political core? "He's really more a Democratic Leadership Council type than a Republican," says Ron Silver. Former Bush White House aide James Pinkerton happily claims Giuliani as a "new paradigm" Republican. Historian Jim Chapin thinks Giuliani is a "progressive-conservative" in the tradition of Teddy Roosevelt, who was a New York City police commissioner before he was president. Giuliani's trust-busting record as a prosecutor, his crime fighting and his gunboat diplomacy with the public authorities make that comparison interesting.

Whether the nation's most raucous and ideologically divided city will claim him as a savior or a victim remains to be seen. Giuliani can't govern amid wrenching contractions without evoking a spirit of shared sacrifice rooted in the perception that he's distributing pain fairly. He hasn't accomplished that yet. Nor has he realized that, unlike a prosecutor's adversaries, who go away once he convicts them, a mayor's defeated opponents and ex-employees are still his constituents, haunting him at the polls, in the streets and on the welfare rolls. "I have to move quickly," he says, "because every day you wait the problems grow exponentially." Including the problems he is bringing on himself.