But what exactly are those ideas? When it comes to the most controversial one being discussed -- banning "assault weapons" -- it's unclear. That's because the term itself is abstract. There is no clear definition of an "assault weapon."
The 10-year so-called assault weapons ban enacted in 1994 named 19 semiautomatic firearms, as well as semiautomatic rifles, pistols, and shotguns with specific features.
"In general, assault weapons are semiautomatic firearms with a large magazine of ammunition that were designed and configured for rapid fire and combat use," the Justice Department said at the time.
That may be the closest thing to a simple explanation the government ever gave, but if you want to see how incredibly complicated the official definition is in the law itself, check out the language.
"I wrote a book on gun control. I don't know what an assault weapon is," Wilson says.
The National Shooting Sports Foundation and other gun enthusiasts complain that what ultimately separated an "assault weapon" from a "non-assault weapon" under the 1994 law was cosmetic.
Some Second Amendment groups and gun retailers prefer the terms "tactical rifle" or "modern sporting rifle."
The term "assault rifle" was first used by Germany during World War II, The New York Times notes. Later, U.S. manufacturers adopted the words as they began to sell firearms modeled after new military rifles.
In today's parlance, adding "military-style" doesn't draw a clear line either.
Sen. Dianne Feinstein, D-California, who has submitted legislation for a new "assault weapons ban," says it would include, among other things, "all semiautomatic rifles that can accept a detachable magazine and have at least one military feature: pistol grip; forward grip; folding, telescoping, or detachable stock; grenade launcher or rocket launcher; barrel shroud; or threaded barrel."
The previous ban included semiautomatic pistols with at least two features, including a detachable magazine, threaded barrel, a shroud allowing the shooter to "hold the firearm with the nontrigger hand without being burned," a weight of 50 ounces or more unloaded, or what was described as "a semiautomatic version of an automatic firearm."
An automatic weapon, as the Justice Department put it, is a machine gun that allows you to fire bullets in succession by holding in the trigger. Fully automatic weapons are severely restricted under existing law, but in some cases they are still legal to own, as the Los Angeles Times notes.
They're commonly used in the military but rarely owned by civilians.
A semiautomatic weapon can load bullets automatically, but it fires only once each time you pull the trigger.
In the effort to prevent mass killings, those pushing for a new assault weapons ban want to halt the production and sale of certain semiautomatic weapons and high-capacity "feeding devices" -- such as magazines -- that allow for a large number of rounds of ammunition.
Feinstein's bill would ban selling, transferring, importing or manufacturing 120 named firearms, certain semiautomatic rifles, handguns, "shotguns that can accept a detachable magazine and have one military characteristic" and "semiautomatic rifles and handguns with a fixed magazine that can accept more than 10 rounds."
During the previous ban, gun manufacturers were able to make cosmetic changes to evade the law. One chief question now is how a piece of legislation could avoid the same happening again.
Can words help bridge the gap?
"If you get new words, there's a better chance of moving beyond the polarization," says Tannen, who is spending this year at Stanford's Center for Advanced Study in the Behavioral Sciences. But, she warns: "Words don't stay neutral for long -- because they quickly get associated with the people that use them."
When asked for a case in which more neutral language may have helped the government reach a consensus on a controversial topic, Tannen said "nothing comes to mind."
Instead, the race is on to control the semantics, which are "crucial," says Wilson.
"In American politics, the person who gets to define the issue wins."