During this month alone, the hollow-eyed Mr Giuliani has astonished New Yorker's by engaging in a highly public brawl with his widely praised Police Commissioner, William Bratton, while at the same time proposing a budget so draconian some believe it would destroy the city's entire welfare edifice.
The dispute with Mr Bratton, who was imported by Mr Giuliani from Boston to head the city's police department, arose from what should have provided glory for both men: statistics showing that in 1994, overall crime in New York was down by 12.3 per cent. It was a figure, however, Mr Bratton chose to trumpet apparently without first informing the mayor's office.
It what seemed a churlish gesture, Mr Giuliani struck back by ordering Mr Bratton to downsize the police department's press office from 28 to 17 - taking it to one fewer than the 18 press officials serving the mayor himself. Mr Bratton was forced to comply, but his own spokesman resigned in a blaze of well-publicised disgust.
Mr Bratton may not have helped himself by, for instance, deciding to reschedule a downtown parade to mark his department's 150th anniversary to coincide with his own birthday. And a gushing profile of Mr Bratton in the New Yorker this month probably did not endear him to the mayor's office. The severity of the mayor's response none the less raised eyebrows.
Among those sounding warnings has been Kevin McAuliffe, a former speech writer of Mr Giuliani's. The former prosecutor, he said, "is a mayor who personalises every policy dispute, equates his own wants and needs to a battle for good against evil and demands an unprecedented degree of control on the working of government".
Concern was also expressed in a New York Times editorial, which began: "When does strong, purposeful leadership slide over the line into ruinous authoritarianism?"
It went on: "There is no question that Rudolph Giuliani has provided direction to what often seemed a rudderless city government ... but there is now a disturbing sense that all the Giuliani administration's accom- plishments are balanced on a knife's edge."
The stakes are highest in the budget debate. With a projected deficit in 1996 of $2.7bn (£1.7bn), and the pool of tax resources shrinking fast, New York is facing a financial crisis at least as serious as the one it confronted in 1976. Like Washington DC, the Big Apple is teetering on the brink of insolvency.
Mr Giuliani's 1996 budget proposals, unveiled last week, represent the biggest cut in government spending in this city since the Depression. Historically, New York's budget has fallen from one year to the next only nine times since the city was incorporated in 1898.
Now the mayor is demanding a $1.3bn reduction in spending next year, equivalent to 4 per cent of the whole budget with the savings coming principally from social safety net policies, including medical payments for the poor, welfare benefits for single mothers and school programmes. At least one of 11 municipal hospitals could close with 20,000 redundancies.
Mr Giuliani, who only last autumn was cheering Democratic hearts by supporting liberal state governor Mario Cuomo against the ultimately successful challenge of Republican George Pataki, seems almost to relish his role as budget Scrooge. "We must choose between pulling ourselves into the late 20th century or remaining mired in the tired and abandoned policies of the Great Society", he said.
For now, his plan has gone into the chambers of City Hall from where a final version will emerge in June.
Meanwhile, Mr Giuliani and Mr Bratton were knocked off the tabloid front pages yesterday by the news of New York Senator Alfonse D'Amato's plans to wed millionairess and television gossip queen, Claudia Cohen.