In a New York Times/CBS News poll last month of 1,110 adults nationwide, 63 percent of respondents said they would favor a ban on high-capacity magazines, while 34 percent opposed the idea. The N.R.A. has repeatedly and staunchly opposed a ban, arguing that it would have no effect on gun violence and that it would leave such equipment in the hands of criminals alone.

In a 2004 report for the National Institute of Justice that studied the impact of the 1994 assault weapons ban (which expired in 2004), the authors found that high-capacity magazines were used in crimes much more often than assault weapons were. They said that guns equipped with those magazines tended to account for a higher share of guns used in the killing of police officers and in mass public shootings, though those are a small percentage of overall gun deaths.

Many gun experts and lawmakers believe the two areas ripe for legislative consensus are a bill that would make background checks for gun buyers nearly universal, and a measure that would create a federal statute against straw purchasing, which would give prosecutors better tools to go after people who buy guns that they sell or give to others to commit crimes.

“If you prioritize things in terms of their value and likelihood of them getting passed,” said James Pasco, the executive director of the Fraternal Order of Police, “I don’t think there is anyone who will tell you that background checks aren’t the most important thing to get done.” Law enforcement officials say that combining background checks and straw purchasing penalties would do much to reduce the criminal use of guns.

But many lawmakers, gun violence experts and victims argue that large-capacity magazines, which gun rights advocates say are convenient for target shooting, increase carnage in shootings. President Obama has called for a maximum magazine capacity of 10 rounds. The police have said that Adam Lanza had a 30-round magazine on his semiautomatic rifle in Newtown.

Mark E. Kelly, Ms. Giffords’s husband, testified before the Senate Judiciary Committee in January that Christina Taylor Green, a 9-year-old girl killed in the Tucson shooting, was shot with the 13th bullet in the assailant’s gun. “I am 100 percent sure these magazines have an effect on the number of people killed,” Mr. Kelly said in a later interview.

Such magazines “are so easy to see as a menace to our society,” said Senator Frank R. Lautenberg, Democrat of New Jersey, who is sponsoring legislation that seeks to ban the sale of magazines of more than 10 rounds.