Congressional hearings planned
Legislators said working with Congress will be paramount in curbing gun violence. California Rep. Mike Thompson told CNN on Tuesday that a ban on high-capacity magazines could garner Republican support, but a full-scale assault weapon ban would be hard to get passed in the GOP-controlled House.
House and Senate committees said they would start holding hearings on gun control measures in coming weeks.
In New York, Democratic Gov. Andrew Cuomo on Tuesday signed into law a series of new gun regulations -- the nation's first since the Newtown shootings.
Both New York's GOP-controlled Senate and Democrat-controlled Assembly approved the measure by overwhelming margins.
It includes a statewide gun registry and adds a uniform licensing standard across the state, altering the current system, in which each county or municipality sets a standard.
Residents are also restricted to purchasing ammunition magazines that carry seven bullets, rather than 10.
Keene derided outlawing high-capacity magazines as "a bidding match" that focuses on the wrong issue.
"So the president says you don't need 30-round magazines. How about a 10-round magazine? Andrew Cuomo says, 'Well, I can do better than that. I'll make it a seven-round magazine,'" Keene said.
"The fact of the matter is the kinds of people who do this, particularly the mentally unbalanced -- who are the most likely people to do it -- shouldn't have any magazines," he said.
"The changes in New York are largely cosmetic," said CNN legal analyst Paul Callan, who described state's existing regulations as "the toughest gun laws in the United States."
Lawmakers in at least 10 other states are reviewing some form of new gun regulations in the new year.