Why aren’t more New Yorkers feeling warmly about Michael Bloomberg?

After all, the mayor established himself as a better-than-reasonable manager. And to his credit, he has shown none of the racial hostility that was the hallmark of his predecessor, Rudolph Giuliani. He has sung with perfect pitch while discussing religious tolerance. He can even come up with an amusing quip, like the one he offered a few weeks ago when he noted that if predictions of the Rapture came true, alternate side parking would be suspended.

However, New York City’s 108th mayor is not captivating most New Yorkers these days. A recent Quinnipiac University poll shows that Bloomberg’s approval ratings have hardly improved from their all-time low. About 40 percent of New Yorkers approve of the mayor’s job performance, according to the recent poll, a slight improvement from the 39 percent that commended him earlier in the year.

The truth of the matter is that Bloomberg’s image is suffering from a number of things. He seems, to many New Yorkers, to be an out-of-touch, corporate-friendly, real estate industry-loving, Manhattan-centric mayor who has overstayed his welcome. Let’s remember that this is the mayor who, after insisting that two terms were plenty for a mayor, championed changing a city law approved by New Yorkers in two referendums so that he could run for a third term. New Yorkers look at the mayor as they would the guest at the dinner party who just doesn’t seem to know when to go home.

After brazenly stampeding into his third term, he continued asking New Yorkers to judge him on his record in education. What followed was one of the most disastrous appointments of his entire mayoralty: He appointed Cathie Black, a corporate executive with virtually nothing in the way of educational experience, to lead the nation’s largest school system. It’s a little like asking Sarah Palin to head the maps department at National Geographic.

But if Bloomberg cares about his legacy, all is not lost. In fact, there are certainly strategies that could help the billionaire mayor to improve his standing among everyday New Yorkers. Perhaps the mayor might take the passion and zeal that he has shown for bike lanes, pedestrian thoroughfares in Manhattan and his own third term and apply it now to championing a vigorous plan to build and develop affordable housing for New York’s working class population.

He might also do more than offer silence on the looming expiration of the rent regulations that affect the lives of more than 2 million New Yorkers.

Despite his initial promises to address these issues, he has done little to nothing to strike at the core of the most vexing difficulty that most working-class and middle-class New Yorkers face in living in the town he governs.

If Bloomberg decides to take up the banner on behalf of affordable housing in a manner that will truly make a dent in New York’s utterly onerous cost of living, it would be a real victory for all New Yorkers. It also might just take the fuel out of the perception that his primary concern is with promoting the quality of life for the well-to-do. At the very least, it would certainly cause his poll numbers to improve.