Updated

President Obama pledged Sunday to make gun control a top priority in his second term and vowed to put his “full weight” behind such legislation.

“I’d like to get it done in the first year,” the president said on NBC’s “Meet the Press.” “This is not something that I will be putting off.”

Democratic lawmakers and some Republicans have called for  immediate action in the aftermath of the Dec. 14 shootings in which 20 first-graders were killed inside a Connecticut elementary school.

Obama said Sunday he would not prejudge recommendations. But he said he was skeptical about the only answer being to put armed guards in schools, as the National Rifle Association has suggested.

The president instead vowed to rally Americans around an agenda to limit gun violence, adding he still supports increased background checks and bans on assault weapons and high-capacity bullet magazines.

"I think there are a vast majority of responsible gun owners out there who recognize that we can't have a situation in which somebody with severe psychological problems is able to get the kind of high capacity weapons that this individual in Newtown obtained and gun down our kids," he said, in the interview taped Saturday. "And, yes, it's going to be hard."

Democratic Sen. Dianne Feinstein, who sponsored legislation that banned assault-style weapons from 1994 to 2004, said immediately after the tragedy at the Sandy Hook elementary school in Newtown, Conn., that she would introduce similar legislation early next year, which would include bans on the high-capacity clips.

Feinstein declined to say on “Fox News Sunday” when she would introduce new legislation, but said it would essentially “strengthen” the 1994  bill.

Republican Sen. Lindsey Graham said he supports armed guards over more gun control and would oppose Feinstein’s legislation

“You can't take every sharp object out of the reach of people like this,” the South Carolina senator told Fox. “I own an AR-15 and I have done nothing wrong by owning the gun. If you had armed security, with better rules of engagement, that, to me, is a better way to deal with the situation.”

Six adult staff members were also killed at the elementary school.

Shooter Adam Lanza committed suicide, apparently as police closed in. Earlier, he had killed his mother at the home they shared.

The tragedy immediately prompted calls for greater gun controls. But the NRA strongly resisted those efforts, arguing instead that schools should have armed guards for protection.

Some gun enthusiasts have rushed to buy semiautomatic rifles of the type used by Lanza, fearing sales may soon be restricted.

The president also said Sunday that he intends to press the gun issues with the public.

"The question then becomes whether we are actually shook up enough by what happened here that it does not just become another one of these routine episodes where it gets a lot of attention for a couple of weeks and then it drifts away," he said. "It certainly won't feel like that to me. This is something that -- you know, that was the worst day of my presidency. And it's not something that I want to see repeated."

In addition, a member of the president's cabinet said Sunday that rural America may be ready to join a national conversation about gun control.

Agriculture Secretary Tom Vilsack said the debate has to start with respect for the Second Amendment right to bear arms and a recognition that hunting is a way of life for millions of Americans.

But Vilsack said Newtown has changed the way people see the issue. "I really believe that this is a different circumstance and a different situation and I think the president believes it as well, that this is going to be sustained convention," Vilsack said on CNN.

Obama also listed deficit reduction and immigration as top 2013 priorities.

The Associated Press contributed to this report.