"IN SOME WAYS THIS IS THE HARDEST CITY TO RUN," SAY New York City Mayor Rudolph Giuliani. "But in some ways it's the easiest if you do the fundamentals right." You want to talk fundamentals? In Manhattan, during Giuliani's administration, serious crime has plummeted by 45 percent and murder by 61 percent, owing in good measure to the mayor's policing reforms. Welfare rolls are down by almost a third. Get those things right, and running the Big Apple is a piece of pie. On Election Day voters in that heavily Democratic city swept their Republican mayor back into office with a massive 17-point win over liberal torchbearer Ruth Messinger. Bipartisan support like that was enough to get political talkers talking about Giuliani for President.

"It's not where my head is right now" is all he'll say about such speculation—though he does admit that "when I look at the Capitol, I get a special feeling about it." Nobody doubts Giuliani has the drive for higher office. The man is so tireless that the editorial page of The New York Times recently told him to get more sleep. "I think what I am is very passionate," he says. "I take the job very seriously." All the same, there are some speed bumps in the way of his forward drive. Earlier this year, Vanity Fair went public with rumors that Giuliani, 53, had indulged in an affair with his 32-year-old communications director, Cristyne Lategano, and was deeply estranged from his second wife, Donna Hanover, 47, a New York City TV personality and sometime actress (The People vs. Larry Flynt). Hanover, the mother of his two kids who was frequently at her husband's side during the 1993 campaign, sat this one out—and even refused to tell reporters which way she cast her vote. The other big question for Giuliani remains whether he is maybe a little bit testy. "His personality is his major defect," says ex-Mayor Ed Koch, who voted for him anyway. This month a Manhattan federal judge told him he could not bar city buses from carrying an ad that claimed New York magazine was the only good thing in the city the mayor had not tried to take credit for. But Giuliani is trying hard to shed the iron-heel image—even if it means putting on high heels. At a city hall press-corps banquet this year, he emerged onstage in full drag. He did it again in November, when he played host—and an Italian grandma—on Saturday Night Live. Memo to Hizzoner: You may look fetching in that floral print house-dress, but before you throw your hat in the ring, lose the curly gray wig.