Supporters of a ban say such weapons have no place in the general public because they are designed solely for rapid-fire killing capacity, rather than hunting or sport shooting.
Right to bear arms
The NRA and other opponents contend that any limit on private gun ownership violates the constitutional right to bear arms. Even partial steps in that direction, such as prohibiting specific models, are considered a path to potential confiscation or other future elimination of Second Amendment rights, they argue.
In recent decades, the NRA has led lobbying efforts that shifted the discussion away from stronger gun controls -- such as an outright ban on handguns and a national registration of gun ownership pushed by top Democrats in the 1980s and 90s -- to the incremental measures under consideration now.
Erickson Hatalsky of Third Way noted examples of the NRA's influence in the last significant gun legislation -- the Brady Bill of 1993 that required background checks on guns purchased from licensed dealers, followed by the limited assault weapons ban a year later.
While the Brady Bill led to the background check system in use today, the NRA made sure it didn't apply to private sales, such as those at gun shows, she said.
Obama and other Democrats now want to close what they call a loophole to make background checks a requirement for any gun sale.
The issue gained prominence after the Columbine high school shootings in 1999 in which three guns used by the two underage killers had been purchased by 18-year-old Robyn Anderson at a Colorado gun show to avoid a background check.
Anderson later told a Colorado House of Representatives committee that the gun purchases had been "too easy."
"I wish it had been more difficult," she said. "I wouldn't have helped them buy the guns if I had faced a background check."
The 1994 weapons ban targeting military style weapons was gone 10 years later, when Congress let it expire in the administration of President George W. Bush -- an outcome sought by the NRA.
Keene and other NRA officials argue the ban failed to reduce gun violence because it targeted firearms used in only a fraction of the nation's gun violence. They also contend the government isn't properly enforcing the background checks created by Brady Bill, making an expansion illogical.
"We are not willing to support measures we feel unduly burden innocent and law-abiding Americans, and on the other side do not have any real impact on the problem we're trying to solve," Keene said.
To Erickson Hatalsky, the goal is to get laws on the books that make it harder for criminals, terrorists and the mentally ill to obtain guns -- either through private sales or from traffickers through straw purchases.
Minor exceptions would apply to family members giving guns to each other, or people borrowing guns on a hunting ground, she said.
"How are they going to stop somebody who's a gun trafficker if there's no federal law against that now," she wondered.
Limits on magazine rounds
A tougher issue involves proposed limits on ammunition magazines to 10 rounds, she said. Larger capacity magazines allow semi-automatic weapons to fire dozens of rounds in seconds.
At a Senate Judiciary Committee hearing on gun control last week, Mark Kelly argued that the proposed limit could have prevented the death of a young girl in the Tucson, Arizona, attack that seriously wounded his wife -- former Rep. Gabrielle Giffords.
According to Kelly, the 13th shot fired killed 9-year-old Christina-Taylor Green, and the shooter got tackled when trying to reload. With a 10-round limit, Green might still be alive, he said.
The NRA and its supporters say larger-capacity magazines are popular, with millions already in the possession of American gun owners who want them to feel secure against criminals armed with similar firepower.
They also contend citizens have the right to such weaponry to protect against future government tyranny, which they say was the intent of the Second Amendment's right to bear arms.
Erickson Hatalsky rejected any inference by the NRA or its supporters that Obama's proposals or other measures being discussed in Congress amount to taking away people's guns.
She praised the president's strategy of presenting a broad package for Congress to consider, saying: "It behooves people who are working on this issue to keep the NRA arguing about lots of different issues, rather than allowing it to concentrate on one and defeat it."