New York City without Ed Koch?

For some - especially Koch, the opinionated mayor of the past 11 years - it's hard to picture. For others, including at least six who want the job, it's easy. And polls and pundits seem to agree: Mayor Edward I. Koch is in trouble.After four years of scandals, AIDS, homelessness, crack, crime and crumbling bridges, many New Yorkers think their No. 1 loudmouth has gone from lovable to laughable to lose-able.

Koch, 64, acknowledges he's not the same man who went from Congress to Gracie Mansion, the mayor's residence, in 1977: "I'm not any smarter - I'm wiser, I hope. I'm more beaten up. I'm just as resilient in terms of coming off the mat and fighting back."

For much of the country, Koch is the book-writing, Donald Trump-taunting, Jesse Jackson-jeering embodiment of the essential New Yorker - obstinate, obnoxious, smart and sort of entertaining. Talks too much.

At home, polls show his Democratic voter support straining to reach 30 percent; half of the voters disapprove of his performance. He'd lose a four-way race for the Democratic nomination, the polls say, and even if he won, he would be defeated by a Republican, former U.S. Attorney Rudolph Giuliani.

But those are just scientific newspaper polls. Koch said his own show-of-hands polls at his public appearances indicate otherwise. "I think there is a reservoir of great goodwill out there and appreciation for what I've done."

Others might disagree. Koch is "on the ropes" (The Wall Street Journal) and his third term "a shambles" (Vanity Fair), partly because of his "mean-spirited, gratuitous, bullying egocentricity" (New York magazine).

And those were relatively even-handed articles.

In the bookstores is "City for Sale," 466 pages dense with details of the corruption scandals that tainted everyone from borough presidents to the Gracie Mansion chef, who used city equipment for his catering business.

Newspapers offer daily doses of criticism - Koch says he's "the whipping post for about six or eight columnists." And a black newspaper, the Amsterdam News, has called for his resignation on its front page for more than 160 weeks.

Koch, however, is planning to become the city's first four-term mayor.

"Now, I don't expect to get the 78 percent majority I got in 1985. That was unique - the highest in the history of the city. But all I need is 51. And I hope to get even better than that," Koch said.

His main challenger for the Democratic nomination is Manhattan Borough President David Dinkins, who leads the polls and would be the first black mayor. Two other Democrats expected to run are city Comptroller Harrison J. Goldin and Richard Ravitch, a builder who has headed the state Urban Development Corp. and the Metropolitan Transportation Authority.

Waiting to take on the survivor is Giuliani, who earned a crime-busting aura by prosecuting mobsters, Wall Streeters and corrupt officials. Giuliani is faced by Ronald Lauder, an heir to the Estee Lauder cosmetics fortune who was ambassador to Austria during the Reagan administration.

"I'm the underdog, and I'm not saying that to get sympathy. All the polls show it," Koch said. What they really show, he feels, is vague dissatisfaction and annoyance with the guy who's been on the television for 12 years.

"My friends and supporters have said, `Listen, one of the things that people say they don't like - in the sense that they once did - is your feistiness. So tune it down,"' he said. "I'm trying. You'll notice my voice is two octaves lower. I'm practicing. And I speak slow."

"The problem for Koch," said former Senate candidate Mark Green, "is that many of his opponents embody a compelling rationale against him.

"Dinkins can credibly argue that he is a quiet healer, not a nasty loudmouth dividing our city. Giuliani can credibly argue that he is a fresh face who will clean up the city, unlike the mayor who looked the other way.

"Goldin is a Koch without the sleaze or the shtick. He's smart, experienced and nervy. Ravitch can persuasively argue that he's an experienced builder who can run without the baggage of being a clubhouse politician."

None has to defend an administration in which six officials appointed by the mayor have gone to jail or been indicted and 200 low-level officials have been charged with wrongdoing.

"I accept full responsibility for everything, good and bad, in my administration," Koch said. "And I say to people: When you judge me, judge me on what you would have done before and what you would have done after. And did I do what makes common sense?"

Koch speaks with pride of his administration's accomplishments: hundreds of millions spent on the homeless, a $5.1 billion program to create 53,000 new and rehabilitated apartments by 1993, millions being spent on Tactical Narcotics Teams of police officers who focus on drug-ridden neighborhoods.

"No city does what we do. We get no credit for it. There is a gap between substance and what people perceive," he said, admitting however that the perception is distorted by his combative nature and sarcasm.

"It may be that people have come to the conclusion that people don't want that sense of humor and other personality aspects," Koch said.