Senator Jorge Luis Preciado's push for wider access to guns has faced resistance in a country where drug cartels have wreaked havoc with illegally-obtained assault rifles.
Even his conservative National Action Party has refused to endorse his proposal. Undeterred, Preciado launched last week a national campaign to collect 120,000 signatures, which would force Congress to look at the constitutional amendment.
The lawmaker seeks to seize on Mexicans' anger and frustration at the dismal state of justice in a country where only one percent of crimes are punished, according to an impunity study by University of the Americas Puebla.
Mexico is "a failed state in terms of security. We aren't asking (the authorities) to defend us. We are telling them, 'Let us defend ourselves,'" Preciado told AFP in an interview in the Senate.
While the law allows Mexicans to possess small-caliber weapons at home for protection, Preciado said it only benefits "a very select group, including soldiers, businessmen, politicians."
The only way to legally buy a firearm is at a store in Mexico City overseen by the defense ministry after obtaining a $115 permit. Only 3,075 gun permits have been authorized in recent years.
Preciado's proposal would allow gun possession inside private businesses and vehicles.
In Mexico City, for instance, thieves take advantage of the mega-capital's notorious traffic jams to rob drivers at gunpoint.
"Today in Mexico you can steal, rob and extort with total impunity. The citizen doesn't have the tiniest possibility to defend himself," Preciado said.
- Vigilante justice -
One man took justice into his own hands on Monday. After four armed people robbed a bus near Mexico City, a passenger pulled out a gun and killed them all, according to witnesses. The shooter then left and disappeared.
An editorial in the newspaper El Universal said such recent acts of vigilante justice show that people are fed up with impunity, but it is also "a virtual adoption of the law of the jungle."
"How many could have saved their lives if they had a gun permit? How many kidnappings, rapes and robberies could have been avoided?" asked Luciano Segurajauregui, regional director of Mexico Armado, an organization that promotes gun possession.
Banning people from defending themselves with guns is "the equivalent of prohibiting the use of fire because it burns or the use of water because it drowns," he said.
Raymundo Moreno, a private security entrepreneur, has called for citizens to be allowed to carry high-caliber weapons like the ones used by criminals.
Some 2,000 guns, assault rifles and grenade launchers illegally enter Mexico through the porous US border every day, according to a study commissioned by the lower house of Congress.
- More deaths? -
For Francisco Rivas, director of the National Citizen Observatory, a non-governmental organization that monitors crime, it remains to be seen if Preciado's proposal is actually "a serious proposal or a mere provocation."
"I don't see it as viable," Rivas said.
He criticized Preciado's argument that there is less crime in the United States than Mexico thanks to legal and widespread firearm possession, which deters criminals.
"The United States is a country where people are armed and there are crimes. There are fewer (than in Mexico) because they have a police force capable of resolving problems," Rivas said.
He said Preciado should instead "invest his time in strengthening the security and justice institutions" of Mexico.
If the lawmaker's plan is approved, Rivas warned, there could be "a lot of deaths that we could blame on one person in particular, which is Senator Preciado and all the senators who decide to support his initiative."