"You can't draw me!" shouts the crude caricature of the Prophet Muhammad, sword raised in one hand. The cartoonist adds one more pencil stroke to the page and responds: "That's why I draw you."

This cartoon by illustrator Bosch Fawstin was the winner of the "$10,000 Muhammad Cartoon Contest and Art Exhibit" held last night in Garland, Texas. Two gunmen were shot and killed by police outside the building where the contest was held. This comes on the heels of the massacre in January of staff at the French magazine Charlie Hebdo, which had published cartoons of Muhammad in the past.

Combining an offensive religious stereotype with a vigorous defense of the First Amendment's right to freedom of expression, Fawstin's cartoon neatly sums up what's at stake in debates over cartoons depicting the Prophet Muhammad that have flared up periodically over the past ten years.

Following incidents like the Garland shooting, Americans tend to come down overwhelmingly in favor of free expression. For instance, a January Pew Research Center survey found that among Americans who had heard about the Charlie Hebdo attacks, 60 percent said it was okay for the magazine to publish the cartoons, compared to only 28 percent who said it wasn't okay.

But there were some notable demographic differences in the response to this question. Whites were significantly more likely than non-whites to say publishing the cartoons was okay. Republicans and the highly educated were more likely to support the cartoons than Democrats and the less-educated. Most interestingly, among age groups Millennials were the least likely to support publishing the cartoons.

More broadly, Americans have consistently supported the right to offensive speech over the years. An AP/GfK survey question from 2008 to 2012 asked respondents whether people should have the right to say what they believe even if they take positions that seem deeply offensive to most people. Each year, Americans responded in the affirmative by more than two-to-one margins.

However, American support for pushing First Amendment boundaries is not absolute. Last year the First Amendment Center found that nearly 40 percent of Americans say the First Amendment "goes too far" in the rights it guarantees, a near-record high. And in 2010 the survey found that while a majority of Americans -- 53 percent -- said people should be allowed to say things in public that are offensive to religious groups, fewer (44 percent) said the same about speech that is offensive to racial groups.

But to the extent that there is a national debate over the propriety of publishing offensive cartoons, it's mostly happening within the media, rather than among the public at large. Cartoonist Garry Trudeau criticized the Charlie Hebdo images as "hate speech" last month. More recently, six writers withdrew from this month's PEN award ceremony, which will honor Charlie Hebdo, and as of last Thursday at least 204 more signed a letter of protest over concern that the award is "valorizing selectively offensive material."

It might seem odd that people whose livelihoods depend on first amendment protections are the most vocal in their opposition to pushing the amendment's boundaries. On the other hand, maybe it makes perfect sense.

Correction: this article originally mis-stated the number of signatories of the PEN America letter.