GOP lawmakers are showing caution on what measures they would back to prevent gun violence, as the gun-rights lobby rejects calls for more restrictions on firearms.

President Obama is urging the next Congress to take action on legislation to stem gun crime, in a concerted attempt to respond to a series of mass shootings this year. The latest incident, at Sandy Hook Elementary School in Newtown, Conn., on Dec. 14, which left 26 dead, including 20 children, has renewed debate on gun control.

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But on Sunday, National Rifle Association (NRA) CEO Wayne LaPierre rebuffed calls for more gun restrictions, saying that they would not prevent future violence.

LaPierre, in an appearance on NBC’s “Meet the Press,” doubled down on a proposal from the nation’s largest pro-gun lobby to push Congress for legislation that would put armed guards in every school.

"If it's crazy to call for putting police in our schools to protect our children, then call me crazy," LaPierre said. "That's the one thing that we can do immediately that will immediately make our children safe."

But so far there is meager GOP support for the solution proposed by the NRA.

Retiring Sen. Kay Bailey Hutchison (R-Texas) wouldn't get behind a federal push to put police in schools, she said.

"I certainly think that at the local level, they should make this decision, because that is going to be accepted in some places and not accepted in some places," she said Sunday on CBS.

Other Republican lawmakers on Sunday carefully suggested that while more school security was a good place to start, there should be a focus on providing mental health care and addressing violence in entertainment.

Sen. Lindsey Graham Lindsey Olin GrahamTrump official releases unverified Russian intel on Clinton previously rejected by Senate panel Barrett says Trump offered her Supreme Court nomination three days after Ginsburg death Supreme Court nominee gives no clues in GOP meeting MORE (R-S.C.) on NBC said that he owned a semi-automatic weapon and questioned if new gun controls alone would be effective.

“I own an AR-15. I've got it at my house. The question is, if you deny me the right to buy another one, have you made America safer? My belief is that this is a problem where you try to get mass murderers off the street before they act, by better mental-health detection. You try to find ways to understand what makes them who they are,” said Graham.

“But I don't suggest we ban every movie with a gun in it, and every video that's violent. And I don't suggest you take my right to buy an AR-15 away from me, because I don't think it will work. And I do believe better security in schools is a good place to start,” he added.

GOP Rep. Tim Scott Timothy (Tim) Eugene ScottAdvising Capitol Hill on insurance Author Ryan Girdusky: RNC worked best when highlighting 'regular people' as opposed to 'standard Republicans' Now is the time to renew our focus on students and their futures MORE (S.C.), who will replace retiring Sen. Jim DeMint (R-S.C.) in the upper chamber in January, also expressed caution over Congress’s next steps, calling both the NRA and Democratic responses “premature.”

Scott suggested that lawmakers wait until the president’s task force on gun violence returned with its findings.

"The president has just established a committee to take a serious, holistic look at what we need to do as a nation to make sure that our kids are safe," he said on CBS’s “Face the Nation.” "I think after we have the committee's report, we should take a very serious look at whatever it takes to keep our kids safe at school.

“After we have those answers, we'll be in a much better position to decide the path forward," he added.

Democrats, though, remained sharply critical of the NRA’s proposal and repeated their strong demands for new gun control.

Sen. Mark Warner Mark Robert WarnerTrump official releases unverified Russian intel on Clinton previously rejected by Senate panel FBI director casts doubt on concerns over mail-in voting fraud Democrats call for declassifying election threats after briefing by Trump officials MORE (D-Va.) said the NRA’s resistance to new gun laws “didn’t pass my gut check,” and noted he was open to a ban on large clips.

Sen. Amy Klobuchar Amy Klobuchar3 reasons why Biden is misreading the politics of court packing Social media platforms put muscle into National Voter Registration Day Battle lines drawn on precedent in Supreme Court fight MORE (D-Minn.) on ABC’s “This Week” said lawmakers knew “we can't have an armed guard at every doorway, at every classroom.” But she expressed support for more background checks to prevent the sale of firearms to the mentally ill and also a ban on high-capacity magazines.

Those who want new restrictions are finding strong support at the White House. Obama has pledged to address gun control in his State of the Union address next year, the first time the issue will be raised in the annual address to Congress in more than a decade.

The move underlines the administration's determination to see "real reform" on guns by January. Obama has asked for Congress to take up very specific legislation that would ban sales of assault weapons and high-capacity ammunition.

That type of legislation is likely to pass the Senate, where even pro-gun Democrats such as Sens. Harry Reid Harry Mason ReidGOP senators confident Trump pick to be confirmed by November Durbin: Democrats can 'slow' Supreme Court confirmation 'perhaps a matter of hours, maybe days at most' Supreme Court fight pushes Senate toward brink MORE (D-Nev.) and Joe Manchin Joseph (Joe) ManchinSenate Democrats want to avoid Kavanaugh 2.0 Energy innovation bill can deliver jobs and climate progress The Hill's Morning Report - Sponsored by JobsOhio - Trump's tax return bombshell MORE (D-W.Va.), who has an "A" rating from the NRA, have been calling to put everything on the table for a "conversation" on gun restrictions.

But whether such legislation would pass the House, where the majority of Republicans are wary of any legislation stepping on Second Amendment rights, is less certain. More than half of the 113th Congress, which begins in January when new members are sworn in, have been rated "A" on gun rights by the NRA, according to The New York Times.

Speaker John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio), who has been given an "A+" rating based on his voting record by the gun lobby, has promised to consider recommendations proposed by a White House task force led by Vice President Biden, who holds an "F" NRA rating.

Polls this week have indicated Americans support banning assault weapons, although gun-control advocates such as Sen. Charles Schumer Chuck SchumerDemocrats rip Trump for not condemning white supremacists, Proud Boys at debate Warren won't meet with Barrett, calling Trump's nomination an 'illegitimate power grab' Schumer won't meet with Trump's Supreme Court pick MORE (D-N.Y.) acknowledge that there is likely a knowledge gap on which firearms would be covered.

Schumer, though, is optimistic that what he calls the NRA’s "extreme" position will actually build broad support for "passing sensible gun legislation in the Congress."

"Trying to prevent shootings in schools without talking about guns is like trying to prevent lung cancer without talking about cigarettes," Schumer said Sunday on NBC's "Meet the Press."

But NRA officials deny that limitations address the real problem, and instead have attempted to refocus on concerns about the mental health system, violence in video games and previous offenders who reacquire weapons, all issues that legislators have raised and that Obama has indicated should be considered as part of a comprehensive approach.

A Gallup poll on Wednesday found that more Americans believe increasing police presence in schools, reforming mental health services and addressing depictions of violence on TV and in games could help prevent future violence than believe in banning assault and semi-automatic guns.

Still, the week following the Connecticut shooting saw the White House petition website flooded with more than 40,000 requests to act on gun violence and high-profile celebrities taking up the renewed push for more restrictions by Congress.

Although Obama has signaled that he is aware of the complexities on addressing gun violence and is looking for a comprehensive approach, all signs indicate that he will not take “no” for an answer on some new restrictions.

Along with the bully pulpit, Obama plans to rally public support to push Congress into action on specific legislation.

"I need your help," he told petition signers in a video response last week. "If we're going to succeed, it's going to take a sustained effort by mothers, fathers, daughters and sons, law enforcement and responsible gun owners, organizing, speaking up, calling their members of Congress as many times as it takes, standing up and saying 'enough' on behalf of all our kids."