In 1981, unless you were living in a cocaine-fueled delusion cultivated at Maxwell’s Plum, there were plenty of reasons to find fault with the governance of New York City, by then under the direction of Mayor Edward Irving Koch for three years.  The mass transit system was a mess; streets and parks were famously filthy. While the mayor had a hand in rescuing the city from fiscal crisis, crime was soaring, making the year one of the most violent New York had experienced. Released in 1981, John Carpenter’s cult film “Escape From New York” was steeped in the assumption that things were sure to get worse, imagining a not-too-distant future in which all of Manhattan had become a maximum-security prison.  Congenitally unable to assume the role of nursemaid administering consolation, Mr. Koch barreled through with a customary orneriness that left him offending one important constituency after another. Appearing at a synagogue late in his first term, he was asked to name a living statesman he greatly admired and responded by naming the Egyptian president, Anwar el-Sadat. When audience members booed him, the mayor told them to “shut up.”  And yet, given all that, early in 1981 Mr. Koch’s approval rating stood at 62 percent, making him one of the most popular politicians in the country. As Neil Barsky, who documented the mayor’s career in the film “Koch,” put it, he practiced street politics as virtually no one had or has. By the end of the year, Mr. Koch had won re-election in a landslide, taking all five boroughs.  Historically, New Yorkers have had a very high threshold for leaders who are blunt, theatrical, arrogant, intermittently or even consistently jerky — in possession of any combination of qualities that easily lend themselves to the shorthand “larger than life.” Earnestness has played less successfully, in part because it is alienating, and doesn’t inspire the kind of rage or impassioned disbelief that, directed at political figures, can be its own source of entertainment and pleasure. (There’s no downside to the fun you can have complaining about a mayor who believes that people who like ferrets require psychotherapeutic treatment.) As happens so often in romantic life, craziness can keep you hooked while sanctimony just makes you stop paying attention.  Occasioning this reflection is the matter of Mayor Bill de Blasio’s declining approval ratings. A Quinnipiac University poll released this month found that only 44 percent of voters approved of the job he was doing, a five-point drop since the beginning of the year and a nine-point drop since he took office in January 2014.  This is in spite of the facts that the city’s seasonally adjusted unemployment rate fell in March, to 6.6 percent from 7.8 percent at the same point last year, and that the number of homeless families is shrinking for the first time in years. According to a March report from the advocacy group Coalition for the Homeless, the number of homeless families with children had declined by more than 300 since December. Last week, the mayor announced an ambitious plan to preserve and improve the city’s public housing, so long ignored, which contains a population larger than Las Vegas’s in deteriorating buildings, 60 percent of them more than 50 years old.  And yet still it is common to hear, among the educated liberals who helped elect him, that Mr. de Blasio hasn’t lived up to his campaign rhetoric, that he hasn’t done much, that he has been a disappointment, that inequality is still very much alive. Of course, if inequality could be rectified in a year, the mayor would be well positioned to run for Moses. The complaints are typically vague, but running through them are problems with style and affect: He’s preachy; he’s late; he lacks charisma; he’s not around.  Among those who disapprove, there are certainly those who do so with greater intensity — preservationists who believe Mr. de Blasio’s affordable-housing initiative will lead to overdevelopment; neighborhood people who believe there has been inadequate planning to support all the proposed construction; black civic leaders concerned that Mr. de Blasio’s interest in criminal-justice reform is waning; rich people who feel offended that he doesn’t involve himself in rich-people things.  In a matter of a several days, Mr. de Blasio managed to rankle both the Rev. Calvin O. Butts III and the event publicist Peggy Siegal. Ms. Siegal, prompted by the mayor’s absence from the Metropolitan Museum of Art’s Costume Institute Ball, told The Wall Street Journal that Mr. de Blasio “had disdain for the striving, successful New Yorkers,” and that “it is a major shortcoming not to mingle with all classes,” as if she were a regular at game night at the Walt Whitman Houses.  The criticism coming from the Upper East Side philanthropic community and the Harlem clerical community is strikingly similar though; both feel betrayed by a posture that suggests that the mayor doesn’t need them. While it isn’t uncommon to lose momentum during a second year in office — Michael R. Bloomberg’s approval ratings fell sharply during his second year as mayor, before reaching a high of 75 percent in his second term — Mr. de Blasio seems to be having trouble making, and keeping, friends. That may have no consequence on his ability to be re-elected, but it could affect his trajectory as a national leader of the progressive movement, a role he seems to relish. Messiahs don’t need voters; they need disciples.  A version of this article appears in print on May 24, 2015, on page MB5 of the New York edition with the headline: Not Insulting Enough to Be Popular . Order Reprints| Today's Paper|Subscribe
The New York City mayor’s decline in public approval may stem from his demeanor more than his policies.