A debate over whether local law enforcement should enforce federal immigration laws is among the emotionally rife questions about illegal immigrants that will stir up New York City’s relatively placid immigration politics next week.

At a conference on Monday organized by John Jay College of Criminal Justice’s Center on Media, Crime, and Justice, proponents of using police to round up illegal immigrants will face off against advocates of giving illegal immigrants official identification cards, job opportunities, and housing.

While such arguments have ripped apart many American communities, they have rarely penetrated New York City’s borders, and organizers say they hope the city will provide a calm backdrop for finding a consensus — or at least a few ideas — to move the debate forward to practical solutions from polemics.

The idea behind the conference is to allow opponents to air their differences, and then get down to the business of finding out where they can agree, the director of the center, Stephen Handelman, said.

“We know where people stand,” he said. “There’s so much heat and so much smoke. We’re trying to get back to those fundamentals.”

Consensus may not come easily.

At one panel, a New York State assemblyman, Greg Ball, who has called for some local prison and police officials to be trained by Immigration and Customs Enforcement to help deport illegal immigrants, will make his case to the mayor of New Haven, Conn., John DeStefano, who has encouraged illegal immigrants to apply for municipal ID cards and bank accounts.

At another presentation, the Immigration and Custom Enforcement special agent in charge of New York, Peter Smith, will defend recent raids and arrests of illegal immigrants. The raids have caused an outcry among immigrant supporters who will appear later in the program — among them, Mr. DeStefano, who said an ICE raid in New Haven that occurred days after he passed his municipal ID card plan was bungled by agents who didn’t get search warrants or notify local officials.

And at some point during the conference, Mr. Ball says he is planning to hold a news conference outside of the building with an organization of September 11, 2001, victims’ families to talk about his plan to deport illegal immigrants who commit crimes. The organization, 9/11 Families for a Secure America, has called for reducing both illegal and legal immigration and ending citizenship for the children of undocumented immigrants born in America. Mr. DeStefano said his program to grant illegal immigrants official city documents is also a crime-fighting effort that was meant to bring immigrant victims forward and engage a sector of his city that had previously been largely disconnected from government. The criminal aliens that Mr. Ball talks about are “not the vast majority of who we deal with,” he said.

“It’s better that we work with those families than isolate ourselves from them,” he added.

Yet Mr. Ball said he defines himself as a moderate in the immigration debate, and said he hopes to find common ground with others at the conference that have embraced illegal immigrants, such as Mr. DeStefano.

“All the hoopla, and all the debate, and the extremes on both sides, they try to turn this into an us versus them,” Mr. Ball said. “I would hope people could agree that the focus needs to be on embracing legal immigration.”

Mr. DeStefano echoed Mr. Ball when it comes to his belief that the federal government needs to take the reins of immigration policy-making from localities such as his.

His ID policy for illegal immigrants, Mr. DeStefano said, “was just frustration with the federal government’s failures.”