The poll was conducted Aug. 27 to 31 with 892 adults. The margin of sampling error is plus or minus three percentage points.  It suggested that Mayor Michael R. Bloomberg, the center’s most ardent and public defender, has not unified public opinion around the issue. Asked if they approved or disapproved of how he had handled the subject, city residents were evenly split.  While a majority said politicians in New York should take a stand on the issue, most disapprove of those outside the city weighing in: Newt Gingrich and Sarah Palin, among others, have tried to rally opposition to the center.  The debate over the religious center has captivated much of the city: 66 percent said they had heard or read a lot about it, and follow-up interviews with respondents showed that the topic was leading to emotional and searching conversations in living rooms and workplaces throughout the city.  “My granddaughter and I were having this conversation and she said stopping them from building is going against the freedom of religion guaranteed by our Constitution,” said Marilyn Fisher, 71, who lives in the Bensonhurst neighborhood of Brooklyn. “I absolutely agree with her except in this case. I think everything in this world is not black and white; there is always a gray area and the gray area right now is sensitivity to those affected by 9/11, the survivors of the people lost.”  Sentiments about the center appear to be heavily shaped by personal background and experiences. Those who have visited mosques or have close Muslim friends are more likely to support the center than those who have few interactions with Islam.  More than half — 53 percent — of city residents with incomes over $100,000 back the center; only 31 percent of those with incomes under $50,000 agree. Protestants are evenly divided, while most Catholic and Jewish New Yorkers oppose the center.  Age also plays a role. Those under 45 are evenly divided (42 percent for, 43 percent against); among those over 45, nearly 60 percent are opposed.  The center’s developers, and its defenders, have sought to portray opponents as a small but vocal group.  The poll, however, reveals a more complicated portrait of the opposition in New York: 67 percent said that while Muslims had a right to construct the center near ground zero, they should find a different site.  Most strikingly, 38 percent of those who expressed support for the plan to build it in Lower Manhattan said later in a follow-up question that they would prefer it be moved farther away, suggesting that even those who defend the plan question the wisdom of the location.  Richard Merton, 56, a real estate broker who lives on the Upper West Side of Manhattan, exemplifies those mixed and seemingly contradictory feelings.  “Freedom of religion is one of the guarantees we give in this country, so they are free to worship where they chose,” Mr. Merton said. “I just think it’s very bad manners on their part to be so insensitive as to put a mosque in that area.”  Opponents offered differing opinions on how far the complex should be built from ground zero. One-fifth said at least 20 blocks, while almost the same number said at least 10 blocks. Seven percent said at least five blocks.  “Personally I would prefer it not be built at all, but if it is going to be built it should be at least 20 blocks away,” said Maria Misetzis, 30, of the Bay Ridge section of Brooklyn.  As the fight over the center escalated from a zoning dispute into a battle in the culture wars, it has splintered New Yorkers along political lines. Seventy-four percent of Republicans are opposed; Democrats are split, with 43 percent for and 44 percent against.  Even though President Obama is highly popular in New York City, residents are divided over his handling of the issue (he defended the center, then seemed to backtrack slightly). Thirty-two percent approve of his approach, while 27 percent disapprove.  It is not clear, however, that any politician is successfully harnessing the strong feelings around the issue. Even though both Republican candidates for New York governor, Rick A. Lazio and Carl P. Paladino, have sought to make the Islamic center an issue in the race, two-thirds of those polled said it would have no influence on how they made their choice for governor. The poll showed that the economy and jobs remained the most pressing concerns.  Yet those who said the issue would affect their vote were four times as likely to support a candidate who is against the center than one who backs it.  The intensity of feeling is greater among opponents. Nearly three-quarters of respondents who disapprove of the project say they feel strongly; only half of those who back it do so.  “Give them an inch, they’ll take a yard,” Ms. Misetzis said. “They want to build a mosque wherever they can. And once they start praying there, it is considered hallowed ground and can’t be taken away. Ever. That’s why we’re having this tug of war between New Yorkers and the Islamic people.”  John Dewey, 65, of the Rego Park section of Queens, expressed his view in more practical terms.  “We can’t say all Muslims are terrorists,” Mr. Dewey said. “There is a huge population of Muslims throughout the world, and we will have to deal constantly with them in the future. If we make enemies constantly, then we will constantly have war.”  An earlier version of a chart with this article, listing the questions and responses for the poll, misspelled the president's given name. It is Barack, not Barak.  Marina Stefan, Dalia Sussman and Megan Thee-Brenan contributed reporting.  A version of this article appears in print on September 3, 2010, on Page A1 of the New York edition with the headline: New York Poll Finds Wariness for Muslim Site. Order Reprints| Today's Paper|Subscribe
The poll indicated that support for a center planned near ground zero is tepid in its home town.