Dunham moved back to clubs, more than 200 appearances a year. To maintain a connection with his fan base, he would use question cards that he had audiences fill out for his performances to build a database, which was tailor-made for the burgeoning World Wide Web. Though he was voted Funniest Male Standup at the American Comedy Awards in 1998, his club work kept him away from his wife and daughters between two and three weeks each month, which put a strain on his marriage, and made paying bills for his expanded family difficult. By 2002, Dunham was hoping to obtain more TV work to raise his profile and ease his standup schedule. Such exposure was elusive until a successful appearance on The Best Damn Sports Show Period, where Dunham and Walter made jokes at the expense of co-hosts Tom Arnold, Michael Irvin, John Salley and John Kruk, generating laughter from them, and giving Dunham much-needed exposure. In 2003, Dunham was the frontrunner to replace Jimmy Kimmel on Fox NFL Sunday, but hosts Howie Long and Terry Bradshaw were not amenable to the idea of being upstaged by a puppet, and, as Dunham tells it, did not provide a welcoming atmosphere to Dunham, nor allow him to speak much during his appearance.
First Comedy Central specialsOn July 18, 2003, Dunham appeared on Comedy Central Presents, his first solo appearance on Comedy Central. During his half-hour piece, he showcased José Jalapeño on a Stick, Walter, an early version of Melvin the Superhero Guy and Peanut, whom Dunham had begun to merchandise into a line of dolls. The appearance was successful, but Comedy Central resisted giving Dunham more airtime, feeling that he was not a good fit for them. By 2005 Dunham decided to gamble on financing his own comedy DVD, Jeff Dunham: Arguing with Myself, which was taped in Santa Ana, California. Dunham’s manager, Judi Brown-Marmel, lobbied the network to air it, pointing to Dunham's drawing power and merchandising profits and arguing that the network needed more diverse content. Surprised by the high ratings of the first Blue Collar Comics concert movie that same year, the network began to reconsider its brand. In late 2006, Comedy Central aired Arguing with Myself, drawing two million viewers when it aired and selling two million DVDs.
In 2007, Dunham appeared as The Amazing Ken with José Jalapeño on a Stick in the Larry the Cable Guy feature film Delta Farce. His second special, Jeff Dunham: Spark of Insanity, was taped at the Warner Theater in Washington, D.C. that same year. It served not only to cement Dunham's stardom but to introduce his most controversial character, Achmed the Dead Terrorist, which became a viral Internet sensation. A clip of Achmed from Insanity attracted over 140 million hits on YouTube, making it the ninth most watched a clip on that website as of October 2009.
By 2008, Dunham's characters had crossed language barriers, with his specials dubbed for audiences in various countries such as France, and Dunham attracting requests for performances in South Africa, Australia, Norway, Denmark, China, and the Middle East. Jeff Dunham's Very Special Christmas Special was taped at the Pabst Theater in Milwaukee, Wisconsin that same year, and premiered on Comedy Central on November 16, 2008, watched by 6.6 million people. It became available on DVD and Blu-ray on November 18, 2008. The special's premiere was the highest rated telecast in Comedy Central's history.
In September 2008, his career reached new heights as he began performing in arenas filled with tens of thousands of people. Dunham was somewhat wary of such large venues but adapted by adjusting the timing of his often rapid exchanges with the puppets so that audience members farthest from the stage could have time to react.
In addition to his comedy specials, Dunham also released his first music album, Don't Come Home for Christmas, on November 4, 2008. It contains original Christmas songs as well as a parody of "Jingle Bells" by Achmed entitled "Jingle Bombs". All the songs, with the exception of "Jingle Bombs", were written and accompanied by Brian Haner, who joined Dunham's act as "Guitar Guy". His first onscreen appearance was in Jeff Dunham's Very Special Christmas Special.
Critical praise and controversyIn January 2008, Dunham was voted by fans the Top Comic in Comedy Central's “Stand-Up Showdown”. He is the only person ever to win the "Ventriloquist of the Year" Award twice, was nominated "Comedian of the Year" by the TNN Music City News Country Awards, and has drawn praise from the Dallas Morning News for his technique and timing. Critics, such as Randee Dawn of The Hollywood Reporter, accused Dunham's characters of being racist caricatures, sexist, and homophobic.
In 2008, a TV commercial for a ringtone which featured 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 ASA 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 ... I'm considering renaming Achmed 'Bill'", he added. 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, some of whom either questioned the wisdom of translating his act into a series or cited Dunham, his previous specials, or ventriloquism itself as reasons for disliking the show.
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 than it would otherwise 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 a 2014 show in Malaysia, the government requested that he not use or name Achmed in his show. Due to the restriction, but to avoid disappointing fans, Achmed was renamed to be "Jacques Merde, the Dead French Terrorist" (Jacques Merde meaning "Jack Shit").