The nation's largest gun-rights lobby, undeterred by heightened criticism in the wake of the Newtown, Conn., massacre, on Sunday ratcheted up its calls for an armed security guard in every school.

"If it's crazy to call for armed officers in our schools to protect our children, then call me crazy," National Rifle Association CEO Wayne LaPierre said on NBC's "Meet the Press." "I think the American people think it's crazy not to do it. It's the one thing that would keep people safe."

The NRA is under fire from Democrats and even some conservatives for its unapologetic response to the school shooting that left 20 first-graders and six adults dead. LaPierre first proposed having an armed guard in every school Friday, just two hours after the nation held a moment of silence for the victims.

With 4 million members and daunting influence in Washington, the NRA has for years helped deter new restrictions on guns. But on Sunday some questioned whether the group's response to the murder of school children will create a backlash.

"I think he's so extreme and so tone-deaf that he actually helps the cause of us passing sensible gun legislation in the Congress," said Sen. Chuck Schumer, D-N.Y. "Trying to prevent shootings in schools without talking about guns is like trying to prevent lung cancer without talking about cigarettes."

President Obama last week appointed a task force led by Vice President Biden to examine policies for preventing mass violence in the future. He also called on Congress to renew an assault weapons ban, to restrict the availability of high-capacity ammunition clips and to expand the use of criminal background checks for those buying weapons at private gun shows.

LaPierre would not commit to working with the task force and said the focus on high-capacity weapons was a pointless exercise. A White House aide told The Washington Examiner that the NRA's tone was "disappointing at a time when a serious discussion is needed."

But some Republicans on Sunday questioned whether Washington leaders could do anything to stop mass shootings by crazed individuals.

"People where I live -- I've been Christmas shopping all weekend -- have come up to me, 'Please don't let the government take my guns away,' " Sen. Lindsey Graham, R-S.C., said on the NBC program. "And I'm going to stand against another assault ban because it didn't work before and it won't work in the future."

Gun control hasn't been a popular issue on Capitol Hill, and it's not clear whether the Connecticut shooting will prompt a change in the nation's firearms laws. Similar tragedies have done little to change public opinion on the issue.

And the NRA's supporters said a politically motivated focus on gun restrictions ignored broader questions about mental health and the cultural acceptance of terrible violence.

"I would make the point when it comes to more restrictions on firearms in our society, that if we go down that path we're going to miss the focal point of providing safety," former Rep. Asa Hutchinson, an Arkansas Republican who is heading an independent NRA panel, said on ABC's "This Week." "I think that is really the wrong debate to have. We've had an assault weapon ban previous in our history. You had school violence continue. It's not restricted to weapons."