NEWARK, March 22 — Craig Carton and Ray Rossi think mental illness is hilarious and Asian-Americans are best mocked with sing-song Chinese accents. The men, hosts of an afternoon radio show called “The Jersey Guys” that is heard here on WKXW (101.5 FM), favor adjectives for politicians that have to be bleeped out.

Two weeks ago, Mr. Carton and Mr. Rossi started “Operation Rat a Rat/La Cucha Gotcha,” a listener-participation game that encourages people to turn in friends, neighbors and “anyone suspicious” to immigration authorities.

They introduced the segment with mariachi music and set the campaign to end on May 5 (Cinco de Mayo), a well-known Mexican holiday.

At the risk of stating the obvious, the phrase “La Cucha Gotcha” is meant to evoke the Spanish word for cockroach.

Here in New Jersey, where 15 percent of the population is Hispanic, reaction to the show has not exactly been positive.

At a news conference Thursday, Hispanic elected officials and others condemned the campaign as “dehumanizing,” “poisonous” and “idiotic,” threatening boycotts of the show’s advertisers unless the Jersey Guys apologize.

“Scapegoating and stereotyping Latinos does nothing but give bigoted individuals a platform to make ethnic slurs and racist comments,” said Assemblyman Wilfredo Caraballo of Newark, calling the campaign a “publicity stunt” that could incite violence against Hispanics.

But anyone expecting an apology was sorely disappointed when Mr. Carton and Mr. Rossi held an on-air news conference a few hours after Mr. Caraballo’s comments. Seeking to profit from the recently ignited firestorm, the Jersey Guys gathered a corps of journalists, most of them Hispanic, in their Trenton studios and gleefully refused to back down. They insisted that the campaign was not anti-Hispanic and that the phrase “La Cucha Gotcha” was inoffensive, likening the song “La Cucaracha” to a lullaby or a patriotic standard like “Yankee Doodle Dandy.”

After calling Assemblyman Caraballo a “pathetic liar,” Mr. Carton repeated his call to deport every illegal immigrant in the country. “If you’re here illegally, you are breaking the law — no better, no worse than the guy who robs the liquor store or the guy who waits to case your house out and robs you of your belongings,” he said. “You are a criminal.”

He went on to blame illegal immigrants for the state’s high property taxes, problems with uninsured drivers and violent crime. He also hinted that illegal immigrants were more likely to become terrorists. “Our country is at war right now, and it’s very important that we protect our kids, and one of the ways you can protect them is to not let undocumented immigrants into this country,” he said.

This is not the pair’s first foray into public eye-poking. Two years ago, the Jersey Guys infuriated Gov. Richard J. Codey by making fun of his wife’s bout with depression. A few months later they made a few enemies in the state’s sizable Asian-American community by mocking Chinese people and saying that foreigners should not be allowed to dictate the outcome of an “American election.” They later apologized for their remarks about Asians, saying that they were just entertainers and that no one should take them seriously.

This time, however, the men say their campaign against illegal immigrants is anything but showmanship. “This operation is not a game, not a contest,” Mr. Carton said. “Our goal is to make New Jersey and the United States of America safer places to live.”

Judging from the cascade of congratulatory calls, the men have tapped into an angry vein in the state, where, according to 2005 census figures, 20 percent of all residents are foreign born, the third highest rate in the country. “This is an invasion,” said one caller, Carmen Perez, who said she had come to this country as a 3-year-old. “I would deport most of them.”

Considering the Jersey Guys’ lack of contrition and the anger among Latino advocates, “La Cucha Gotcha” is likely to spark an even larger backlash. That may or may not be a bad thing for the station, which, like the entire broadcast radio industry, has been struggling to compete against the twin scourges of electronic music downloads and satellite radio. Eric Johnson, the station’s program director, declined to comment, saying he wanted to give the last word to the Jersey Guys.

But Jack Plunkett, an analyst who follows broadcast radio, said the station might want to check out recent marketing data indicating that Hispanics are the fastest-growing group in the country, with spending power of $700 billion a year, a figure that is expected to triple by 2010. “These guys might not realize it,” he said, “but they could be shooting themselves in the foot.”

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