Democratic legislators have said military-style assault weapons should be banned and that a national commission should be established to examine mass shootings in the United States.
The proposals were among the first to come from Congress in the wake of Friday’s massacre at a school in Newtown, Connecticut.
Gun rights activists remained largely quiet on the issue, all but one declining to appear on Sunday talk shows.
Meanwhile, Democrats vowed action and said it was time to hear from voters on how to prevent the next shooting.
The time for “saying that we can’t talk about the policy implications of tragedies like this is over,” said Chris Murphy, a Connecticut Democrat who won a Senate seat in the November elections.
New York mayor Michael Bloomberg said Mr Obama could use executive powers to enforce existing gun laws.
“It’s time for the president, I think, to stand up and lead and tell this country what we should do not go to Congress and say, ‘What do you guys want to do?’,” Mr Bloomberg said.
Senator Joe Lieberman, an independent former Democrat from Connecticut who is retiring, supports such a ban on assault weapons, but said there should also be a national commission to scrutinise gun laws and loopholes, as well as the US mental health system and the role that violent video games and movies might play in shootings.
Louie Gohmert, a Texas Republican, was the sole representative of gun rights’ activists on the various Sunday political talk shows.
He defended the sale of assault weapons and said that the principal at Sandy Hook Elementary School, who authorities say died trying to overpower the shooter, should herself have been armed.
“I wish to God she had had an M4 in her office, locked up, so when she heard gunfire, she pulls it out and she didn’t have to lunge heroically with nothing in her hands.”