(CNN) -- Sen. Barack Obama's campaign has sharply criticized The New Yorker magazine over the publication's latest cover illustration, which appears to portray the presumptive Democratic presidential nominee and his wife as terrorist enemies of the United States.
The New Yorker cover published Sunday shows Barack and Michelle Obama with a flag burning in the fireplace.
The cover, published Sunday, shows Obama in the Oval Office dressed in traditional Muslim attire. His wife, Michelle, wears an Afro hairstyle and has a machine gun slung over her back. An American flag can be seen burning in the fireplace, and a picture of Osama bin Laden hangs on the wall.
"The New Yorker may think, as one of their staff explained to us, that their cover is a satirical lampoon of the caricature Sen. Obama's right-wing critics have tried to create," Obama spokesman Bill Burton said in a statement. "But most readers will see it as tasteless and offensive. And we agree."
David Remnick, the longtime editor of the highly-regarded publication, told CNN's "The Situation Room" that he believes the ironic intent of the illustration will be clear to most Americans.
"The idea is to attack lies and misconceptions and distortions about the Obamas and their background and their politics. We've heard all of this nonsense about how they're supposedly insufficiently patriotic or soft on terrorism," the The New Yorker editor said.
"That somehow the fist bump is something that it's not. And we try to put all of these images in one cover, and to satirize and shine a really harsh light on something that could be incredibly damaging." Watch talk show hosts discuss the cover »
On Sunday evening Obama campaign spokesman Bill Burton called it "tasteless and offensive." Sen. John McCain said Monday it is "totally inappropriate."
Obama refused to comment on the illustration Sunday.
Obama supporter and Los Angeles City Councilman Bernard Parks Sr. on Monday called for a boycott of the magazine. Parks is a Democratic superdelegate from California.
"I think it's outrageous that we'd have a cover that would depict racism, sexism, anti-religion, also anti-patriotism, and then on top of it to try to draw a conclusion that Mr. Obama has some sympathy toward terrorism," Parks told CNN.
But Remnick, who has approved several provocative covers in the past -- including a recent illustration of Iranian President Mahmoud Ahmadinejad appearing to solicit gay sex in a bathroom -- says he isn't concerned Americans will misunderstand the illustration.
"I think you underestimate the intelligence of the American people, to be quite honest. Yes, there will be some people who will misunderstand it, not get it at first," he said. "But here we are on television, discussing something that's been a kind of subterranean theme in American politics, which is disgusting -- these lies about Barack Obama, about Michelle Obama.
"And so in fact we're not even satirizing the Obamas, we're satirizing these rumors, the lies that have fed into the politics of fear."
Remnick also defended his publication's use of satire in general, likening it to the work of popular television hosts Jon Stewart and Stephen Colbert. "If there's no possibility for satire, if you always have to look for the joke that every -- absolutely everyone will get, you won't have Jon Stewart, you won't have Stephen Colbert," he said.
"Stephen Colbert goes on and mocks right-wing commentary by pretending to be a right-wing commentary. In a way this is Colbert in print."
And not everyone finds the illustration over the top.
"Do you really believe that if you see this ... cover, you're going to say to yourself, 'Oh, this is Barack and Michelle'?" conservative radio talk-show host Shelley Wynter asked. "This is satire. Anybody that looks at a drawing of a cartoon and wants to say, 'This is what my presidential candidate is going to be like' is already ridiculous and shouldn't be voting."
The cover is linked to a feature article about Obama's formative political years in Chicago.
Liberal radio talk-show host Laura Flanders told CNN's "American Morning" on Monday. "I think the Obama campaign made a misstep here. They should have come out strongly endorsing this cover." iReport.com: Satire or slander? Share your thoughts
She said, "This isn't a jab at them, terrorist or any other kind. This is a jab at the media. ... It should be cause for our conversation to focus on the kind of fear mongering that the media and people on the right have engaged in."
Conservative talk-show host Joe Pagliarulo agreed.
"I think this could be a very positive thing for the Obama campaign," Pagliarulo said. "I think they've got to embrace this and say 'Look, there are rumors out there.' I talk to people every day, like Laura does. People really do believe ... that he's a Muslim. They believe he was sworn in on the Quran. They believe that his wife is unpatriotic and so is he."
Conservative talk-show host and CNN contributor Bill Bennett said he understands why the Obama campaign is upset with the cover. "The New Yorker blew this," he said. "It has a distinguished history and great writing. I read The New Yorker occasionally. But it was tasteless and stupid. The intellectuals missed it ... and it backfired on them. If I were the Obama campaign, I would be furious at these people."
But Democratic strategist and CNN contributor James Carville defended the magazine's cover choice as satire in its "ultimate form."
"I don't know what the big deal is," he said.
A Newsweek poll released Friday showed that 12 percent of those polled believed Obama was sworn in as a U.S. senator on a Quran, and 26 percent believed that he was raised as a Muslim.
Neither is true.