WASHINGTON — Recalling the shooting rampage that killed 20 first graders as the worst day of his presidency, President Obama pledged to put his “full weight” behind legislation aimed at preventing gun violence.

Obama voiced skepticism about the National Rifle Association’s proposal to put armed guards in schools following the Dec. 14 tragedy at Sandy Hook Elementary School in Newtown, Conn. The president made his comments Saturday in an interview that aired Sunday on NBC’s “Meet the Press.”

Instead, the president vowed to rally the American people around an agenda to limit gun violence, adding that he still supports increased background checks and bans on assault weapons and high-capacity bullet magazines. He left no doubt it will be one of his top priorities next year.

“It is not enough for us to say, ‘This is too hard so we’re not going to try,’” Obama said.

“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. “And, yes, it’s going to be hard.”

The president added that he’s ready to meet with Republicans and Democrats, anyone with a stake in the issue.

The schoolhouse shootings, coming as families prepared for the holidays, have elevated the issue of gun violence to the forefront of public attention. 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 is strongly resisting 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.

Obama seemed unimpressed by the NRA proposal. “I am skeptical that the only answer is putting more guns in schools,” he said. “And I think the vast majority of the American people are skeptical that that somehow is going to solve our problem.”

The president said he intends to press the issue 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,” Obama 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.”

Separately, 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 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,” Vilsack said on CNN.

Vilsack said he thinks it’s possible for Americans to come together. “It’s potentially a unifying conversation,” he said. “The problem is that these conversations are always couched in the terms of dividing us. This could be a unifying conversation, and Lord knows we need to be unified.”

Besides passing gun violence legislation, Obama also listed deficit reduction and immigration as top priorities for 2013. A big deficit reduction deal with Republicans proved elusive this month, and Obama is now hoping Senate Democratic and Republican leaders salvage a scaled-back plan that avoids tax increases for virtually all Americans.

In addition, he issued a defense of former Republican Sen. Chuck Hagel of Nebraska, who has been mentioned as one of the leading candidates to replace Leon Panetta as defense secretary.

Hagel supported the 2002 resolution approving U.S. military action in Iraq, but later became a critic of the war. He has been denounced by some conservatives for not being a strong enough ally of Israel. Also, many liberals and gay activists have banded against him for comments he made in 1998 about an openly gay nominee for an ambassadorship.

Obama, who briefly served with Hagel in the Senate, stressed that he had yet to make a decision but called Hagel a “patriot.”

Hagel “served this country with valor in Vietnam,” the president said. “And (he) is somebody who’s currently serving on my intelligence advisory board and doing an outstanding job.”

Obama noted that Hagel had apologized for his 14-year-old remark on gays.