Some have accused Dunham's characters of being racist caricatures, sexist, and homophobic. In 2008, a TV commercial for a ringtone featuring Dunham's character Achmed the Dead Terrorist (see Characters below) was banned by the South African Advertising Standards Authority after a complaint was filed by a citizen stating that the ad was offensive to Muslims, and portrayed all Muslims as terrorists. Dunham responded that "Achmed makes it clear in my act that he is not Muslim." However, the Advertising Standards Authority noted that the name Achmed was of Arab origin and was one of the names of Muhammad. Dunham responded, "I've skewered whites, blacks, Hispanics, Christians, Jews, Muslims, gays, straights, rednecks, addicts, the elderly, and my wife. As a standup comic, it is my job to make the majority of people laugh, and I believe that comedy is the last true form of free speech." He further commented, "I'm considering renaming Achmed, 'Bill.'" Dunham has conceded that he does exhibit particular sensitivity to the "conservative country crowd," or those characterized by "basic Christian values," as they are one of his largest constituencies, and part of his upbringing.
Dunham was heckled and criticized for mocking TV critics during a July 2009 press tour to promote his then-upcoming Comedy Central TV series, "The Jeff Dunham Show", as well as Comedy Central programming chief Lauren Correo. In October 2009 "The Jeff Dunham Show" enjoyed good initial ratings, but was not well liked by critics, who did not find it funny, and either questioned the wisdom of translating his act into a series, or conceded a prejudice against Dunham, his previous specials, or ventriloquism itself.
J.P. Williams, the producer of the Blue Collar Comedy Tour, has opined that Dunham's act is not funny on its own merits, and that his material gets a greater reaction because of the puppet characters that it would otherwise not garner by itself. Blue Collar veteran Bill Engvall, a friend of Dunham's insists otherwise, saying that Dunham is inherently funny with or without the puppets.
In 2003, BRASMA Publications released "Dear Walter", a collection of questions asked of Dunham's fictional curmudgeon at live performances, authored by Dunham, and Walter Cummings.
Dunham's autobiography, "All By My Selves: Walter, Peanut, Achmed and Me", was published by Dutton in November 2010.
Walter is a retired, grumpy old man with arms always crossed in discontent. Dunham was inspired to create Walter when he watched Bette Davis' final appearance on "The Tonight Show with Johnny Carson", giving her honest, unfiltered candor to Walter, and patterning Walter's frown on Dunham's own. He has a brash, negative and often sarcastic view on today's world. He is a Vietnam War veteran and a former welder, and "doesn't give a damn" about anyone, especially his own wife and certain audience members. Walter has appeared in all four Comedy Central specials. He's been married for several decades, and when Dunham asks him if he remembers the happiest moment of his life after Walter tells him he has been married for forty-six years, Walter responds, "Forty-"seven" years ago!" Dunham created the Walter puppet himself, including both the initial sculpture and the silicon mold, though he eventually began using professional effects companies for the latter stages with his subsequent puppets.
Peanut is a hyperactive, purple-skinned "woozle" with white fur covering most of his body, a tuft of green hair on the top of his head, and one sneaker on his left foot. Dunham explains in "Arguing with Myself" that Peanut is from a small Micronesian island, and that they met in Florida. Peanut's humor is not based on a particular motif or stereotype, as those of the other characters, and has been described as "the bad kid". He often makes fun of Dunham, and torments and mocks José Jalapeño on a Stick. Touching upon his unusual appearance and personality, he asks Dunham in "Arguing with Myself", after Dunham denies ever having done drugs, "Then how the hell did you come up with "me"?"
José is a talking jalapeño pepper on a stick who wears a small sombrero. José, who speaks with a thick Latin accent, is typically paired with Peanut, who often makes fun of José, uses appeals to Latino stereotypes when doing so, and makes fun of his being on a stick. Although José was not Dunham's first puppet, it was the first that Dunham made himself.
Bubba J is a beer-drinking redneck that Dunham describes in "Arguing with Myself" and "A Very Special Christmas Special" as "white trash trailer park", and whom Dunham uses for humor centered on such stereotypes. To this end, he frequently does jokes involving Bubba J's love of drinking beer and NASCAR, and his low intelligence. Touching upon such stereotypes, Bubba mentions in "Arguing with Myself" that he met his wife at a family reunion, and remembers seeing her with a corn dog in one hand, a beer in another, and leaning against a ferris wheel, "making it tilt". Although he does not appear onstage, Bubba has a prominent role as the backstage security guard in "Controlled Chaos".
Dunham introduces Sweet Daddy Dee in "" as his "new manager". He calls himself a "pimp", which he says stands for "Player In the Management Profession." According to Sweet Daddy, because he is a pimp, that makes Jeff the "ho". When Dunham objects, Daddy Dee points out that Dunham makes people laugh and feel good for a living. When Dunham agrees that this is the case, Daddy Dee says, "You a ho." When Dunham asks what he would say if he told him that he was a comedian only because he enjoyed it, Daddy Dee responds, "You a "dumb" ho."
Melvin wears a blue superhero costume, and is used to poke fun at superheroes. When asked about his superhuman powers, he indicates that he has X-ray vision, adding, "I love looking at boobies!" He appears to have no other powers, however: When Dunham asks how far he can fly, he responds, "How far can you throw me?", and when asked if he can stop a bullet like Superman, he responds, "Yeah. Once." Dunham portrays Melvin as unimpressed with other superheroes: When told Superman can leap tall buildings in a single bound, Melvin dismisses him as a "showoff," arguing that he can simply walk around them, observes that Aquaman has the same powers as SpongeBob SquarePants, asserts that the Flash's super speed is derived from methamphetamine, that the Hulk's vaunted ability to get stronger as he gets angrier merely mirrors "every white trash guy on "COPS"," and makes innuendo about the questionable relationship between Batman and the underage Robin. Melvin's first onscreen appearance was in the July 2003 "Comedy Central Presents" episode, in which he had small, black, beady eyes. By his next appearance, in "Spark of Insanity", he had been modified to have large, blue, crossed eyes. He also has an enormous nose, which he claims is his symbol, and whose similarity in shape to that of a penis is alluded to in the act. Dunham sculpted the current version of Melvin's head himself, and hired an effects company called Renegade Effects Groups to create the rubber mold and complete the puppet, before then installing the mechanics himself.