The last time Mayor Bloomberg ran for office he asked New Yorkers to vote for him on faith.

The billionaire businessman argued that the skills that permitted him to build a successful company would help him get New York City back on its feet after the September 11 attacks. By a slim margin, voters decided to let him try.

This time, as he reminded reporters last week, Mr. Bloomberg has “got a record to run on.” Among other things, that means he will be facing opponents who disagree with choices he has made while in office.

Mr. Bloomberg’s detractors are a motley coalition of New Yorkers: Hispanics who believe his program to end “social promotion” in the schools unfairly prevents many immigrants’ children from entering the fourth grade; conservatives who haven’t forgiven him for raising taxes; Libertarians who hate the smoking ban, and finally those on the West Side who stand against his plans for a massive redevelopment of their neighborhood, including a new Jets football stadium.

“Anyone who is running will have to bring together these people,” the president of the political consultancy the Advance Group, Scott Levenson, said. “Every constituency is critical because, as we saw last time, Bloomberg’s margins are small. Registered Democrats outnumber Republicans 5-to-1, so Bloomberg has that going against him before he even starts. If an opponent can put 6,000 votes together here and 10,000 votes there – well, it won’t take much to make Bloomberg lose the election.”

Mr. Bloomberg’s campaign aides appear to be aware of the problem. They sought to shore up support in the Hispanic community last week by rolling out an endorsement from Herman Badillo, a former congressman and City University chancellor who ran against Mr. Bloomberg four years ago.

Mr. Badillo, a Latino, has long been an advocate of ending the practice of promoting children to higher grades when they can’t meet minimum academic standards. He has called such social promotion a scourge in the school system. Mr. Bloomberg, for his part, has vowed to end it for third- and fifth graders. That has angered some Hispanic parents who feel their children are being unfairly picked on. Mr. Badillo seemed to be willing to give the mayor political cover.

“I’ve been working with Mayor Bloomberg on the issue of social promotion,” he said. “I’m the one who has been pushing this.”

Mr. Bloomberg has a more difficult time distancing himself from higher property taxes. He proposed a 25% increase two years ago and persuaded the City Council to enact an 18.5% increase. While he has returned some of that money in the form of a $400 property-tax rebate, many Republicans are still grousing. More recently they have been upset by the mayor’s reticence to cut city spending and bring taxes down.

In his latest budget, introduced Thursday, Mr. Bloomberg vowed to cut just $500 million from city spending. On the tax-cut side he promised to renew the $400 property tax rebate and said he will work with the governor to make sure an “emergency” personal-income tax and a tax on clothing and shoe purchases of less than $110 sunset on time. He didn’t offer any new tax relief, however.

Two other issues likely to haunt Mr. Bloomberg in November are his two-year-old smoking ban and his plan to develop the lower West Side to make room for an enlarged convention center, office space, parks, and a new football stadium for the New York Jets.

The smoking ban was seen by many New Yorkers as government intervention run amok. While polls show the majority of New Yorkers are in favor of smoke-free restaurants, bars, and offices, the city’s Nightlife Association has been a vocal opponent of the action. That constituency is likely to support anyone but Mr. Bloomberg in November, analysts said.

They could be joined by stadium opponents. Two of the Democratic contenders for Mr. Bloomberg’s job, the former Bronx borough president Fernando Ferrer and Council Speaker Gifford Miller, have called on the mayor to hold a referendum on the stadium plan in November. Mr. Bloomberg has refused, saying that it could hobble the city’s chances to win the 2012 Olympics. Critics say Mr. Bloomberg doesn’t want a referendum on the stadium because he knows he’d lose.

Another political consultant, George Arzt, said that while these groups are all prepared to stand foursquare against the mayor, it isn’t clear whom they’d back instead. There isn’t a single candidate who could catch all the disaffected Bloomberg voters.

“Bloomberg is going to get probably Manhattan, Staten Island, a good part of Queens, maybe Park Slope and that area in Brooklyn,” Mr. Arzt said. “He’ll get a part of the Latino vote, but Freddy will get the big numbers there. Bloomberg will have to use the incumbency to maintain his base in Manhattan, Queens, and Staten Island and just be the better alternative in the rest of the city to come out on top. This race is his to lose.”

The 2001 election numbers show just how tight the race may be. Mr. Bloomberg won 47% of the Hispanic vote in 2001. Turnout among Hispanics was depressed. If the mayor ends up facing Mr. Ferrer, he is likely to see his Hispanic support cut as low as the teens and Hispanic turnout rise, analysts said.

“The key is whether someone else can manage the city better than the incumbent,” Mr. Arzt said. “That will be more important than a stadium or how schools are doing.”