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Following the January shooting of Rep. Gabrielle Giffordsin Tucson, Ariz., Mr. Green decided that Laughter Against the Machine should travel to the state to perform a “rapid-response comedy show,” in the same way guitarist Tom Morello and rapper Kanye West have visited Occupy Wall Street.

As the group discussed the idea, they realized there were other political hotbeds they wanted to visit. Such as New Orleans. And Washington. And Dearborn, Mich., home to the United States’ largest Muslim population.

At each stop on their tour, the comics — who are filming a documentary of their journey — attempt to do more than just tell jokes. In Madison, Wis., they met with union activists, and in New York City, they spent time with protestors in Manhattan’s Zuccotti Park.

In Arizona, the trio went to the border city of Nogales, where they visited a Jesuit-run humanitarian clinic. They saw a presentation about the bodies of illegal immigrants being bundled up in the desert. They went through a Border Patrol checkpoint. They heard a presentation from an American Indian tribe whose historical territory encompasses both sides of the United States-Mexico border.

“Frankly, it was incredibly upsetting,” Mr. Green said. “I’ve traveled in Latin America. It reminded me of being there — being in a militarized society, in the sense that you felt like someone next to you could get ‘disappeared’ at any minute.”

Firsthand, on-site engagement with their comedic subject matter is necessary for Laughter Against the Machine, Mr. Green said, because the group is attempting to transcend the brand of political comedy practiced by late-night talk shows, in which the jokes are never more than superficially political, if at all.

“It’s all about making fun of foibles, but not attacking the feelings or ideas of the people involved,” Mr. Bell said. “In the Clinton era, political comedy was an excuse to repackage a bunch of [oral sex] jokes. Even now, there’s a sense that if you do left-wing comedy, you’re just going to say ‘Sarah Palin is dumb,’ and people will clap.”

To illustrate the contrast with his group, Mr. Bell cited one of Mr. Green’s jokes: Rep. Michele Bachmann, Minnesota Republican and a presidential hopeful, strikes him as someone who is one generation removed from baking muffins for a lynching.

“A liberal audience wants to hear you make fun of Bachmann, but they don’t want to hear about lynchings or women baking,” Mr. Bell said. “The joke requires a sense of humor about yourself and a sense of history. It’s asking a lot of an audience.”

The mind boggles at what the joke asks of a conservative audience.

“I talk a lot about race and identity politics,” said Mr. Bell. “After a while, people are like, ‘Man, I hope he moves on to how airports are weird places or the differences between men and women.’ But we want to carve out our own space in comedy.”

Of course, doing so isn’t easy: At Occupy San Francisco, Mr. Green became the first comedian to tell a joke via the famed “human microphone” system, in which demonstrators repeat what someone has said.

“People laughed, but honestly, it was a disaster,” he said. “It turns out that standing outside on a tarp with people drumming nearby is not the best way to tell jokes. I ended up yelling at people through a bullhorn.”

Mr. Green noted the irony.

“I’ve committed my life to supporting progressive causes,” he said. “But I know how much our side shoots itself in the foot. And I want to be able to talk about that.”