The Entertainment Software Association, which represents publishers of video games, issued a statement opposing the measure.
"We are disappointed that even in the wake of an overwhelming decision in the United States Supreme Court finding proposals such as this to be patently unconstitutional, there are those who still try to attack video games with outdated notions of our industry," said ESA spokesman Dan Hewitt.
In 2011, the U.S. Supreme Court struck down a law in California that banned the sale of violent video games to minors. Most retail stores, including Walmart and Gamestop, already have policies prohibiting underage shoppers from buying mature-rated games.
One obvious problem with Franklin's measure is that the ESRB rates games based on other factors, such as gambling, language, sexual content and drugs and alcohol, says Patrick Ishmael, a policy analyst at the Show-Me Institute. Descriptions on the back of each software title clearly state which factors contribute to the game's rating.
"In other words, teen-rated games like 'The Sims,' 'Dance Central' or 'Guitar Hero' would be included in the tax, even though they're non-violent," he said. "Clearly, the law is poorly crafted. It's probably unconstitutional anyway since it targets the content of speech."
Oklahoma Democratic Rep. William Fourkiller pushed similar legislation in the Sooner State last year, but a subcommittee threw it out by a narrow margin. His initial proposal would have imposed the same 1 percent sales tax, but Fourkiller later revised it to create a task force to analyze the impact of video games on children instead.
Video games have taken some heat after the recent mass shootings. Again, the "Grand Theft Auto-made-me-do-it" excuse is mentioned.
Constitutionally speaking, Ishmael disdains that rhetoric.
"I have a problem with people trying to protect the Second Amendment by throwing the First Amendment under the bus," he told Missouri Watchdog.
As part of a fact-finding mission on the causes of gun violence, President Obama on Wednesday called for studies into software used on Nintendo, Xbox and PlayStation game systems.
One of the best selling-series on all of those platforms, "Call of Duty," pits players against each other online in a series of "deathmatches," in which users can choose from a variety of military weapons. Those games are rated mature.
"Congress should fund research on the effects violent video games have on young minds," Obama said. "We don't benefit from ignorance. We don't benefit from not knowing the science."
Franklin's bill would set aside the additional tax revenue "solely for the treatment of mental health conditions associated with exposure to violent video games."
A representative from her Capitol office told Watchdog on Thursday that Franklin was working on some revisions to her bill, but she didn't say what they were and when the bill would be resubmitted.
The legislation must be referred and approved by a committee before reaching the House floor.