"Restrictions on probably the most popular firearm in America are going to be hard over the long term to square with the right to keep and bear common firearms," said Hoffman, whose group provides education and legal assistance to gun owners.
Gun-control activists say they are confident both types of restrictions would pass constitutional muster.
"The Second Amendment is not an issue," said Jonathan Lowy, director of the Legal Action Project at the Washington- based Brady Center to Prevent Gun Violence.
"The Supreme Court was crystal clear that, while the Second Amendment protects the right of law-abiding citizens to have a gun in the home for self-defense, it also allows for a wide variety of sensible gun laws."
Winkler said that, under Heller, popularity isn't enough to ensure constitutional protection.
"Heller said that handguns are protected because they are in common use for self-defense, not because they're common but because they're common for self-defense," he said.
Andrew Arulanandam, a spokesman for the National Rifle Association, declined to comment on the legal prospects for new legislation. The gun-rights lobby said Wednesday it will hold a "major news conference" on Friday.
So far, federal courts have invalidated only what Winkler called "clear outlier" laws.
On Dec. 11, three days before the Connecticut shooting, a federal appeals court in Chicago struck down an Illinois law that bars most people from carrying a loaded gun except in their home or place of business. Illinois is the only state with an outright ban on carrying a loaded weapon in public.
Writing for the majority in the 2-1 decision, Judge Richard Posner said the Second Amendment offers protection beyond the home. That reasoning put the Chicago court in conflict with a different federal appeals court, which had upheld that state's limits on who can carry a weapon in public.