Users are being asked to vote on their favorite, the creator of which will receive a $10,000 development deal with JibJab.
JibJab, founded by the brothers Gregg and Evan Spiridellis, came to Web fame in 2004 with "This Land," a short animated video parodying the presidential election. The brothers later created a sequel to "This Land," which debuted on "The Tonight Show with Jay Leno."
This April, JibJab launched JokeBox, an online community for comics. The Spiridellis brothers also distribute an e-mail newsletter with around 700,000 opt-in subscribers.
Verizon and other mobile carriers have built out their content offerings this year. In April, Verizon Wireless tapped Heavy.com for comedic shorts.
Verizon rival Sprint last month kicked off its own initiative to produce mobile content. Sprint launched its "Power View" network with seven shows covering the NFL, entertainment news and gossip, and New York's Fashion Week, among other topics.
While wireless carriers compete to build out their content offerings, consumers have been slow to embrace mobile video. Research and consulting firm Telephia recently estimated that mobile TV counted about 3.7 million consumers in the second quarter of this year.