Former Rep. Beto O’Rourke’s call for a mandatory buyback of military-style “assault rifles” raised concerns on both sides of the gun debate Sunday, while Democrats on Capitol Hill continue to push President Trump on their universal background checks bill.

The Texan and 2020 Democratic presidential contender went viral during last week’s debate for enthusiastically calling for a mandatory buyback plan for military-style guns.

“Hell yes, we are going to take your AR-15, your AK-47, we are not going to allow it to be used against our fellow Americans any more!” he said.

However, his message wasn’t embraced by all Democrats, fearing he had confirmed a longstanding Republican charge about banning and confiscating guns that liberals have dismissed as exaggerated.

Rep. David Cicilline of Rhode Island, who is the lead sponsor on an assault-weapons ban in the House that doesn’t confiscate such existing rifles, said Mr. O’Rourke’s remarks weren’t helping the push for stronger gun laws.

“I think that message doesn’t help,” Mr. Cicilline said on “Fox News Sunday.” “That’s just not true. There’s no proposal like that in the Congress.”

South Bend, Indiana, Mayor Pete Buttigieg, and fellow 2020 candidate speaking on CNN’s “State of the Union,” replied “yes” when asked whether he thought such comments are “playing into the hands of Republicans.”

“When even this president and even [Senate Majority Leader] Mitch McConnell are at least pretending to be open to reforms, we know that we have a moment on our hands,” he said. “Let’s make the most of it and get these things done.”

Republicans seized on Mr. O’Rourke’s remarks, with House GOP leadership telling reporters at their policy retreat in Baltimore on Friday that it was one of most concerning moments of the night.

Despite the blowback from both sides of the aisle, Mr. O’Rourke doubled down on his position Sunday, saying fear of the NRA has weakened lawmakers in the capital.

“I think this just shows you how screwed up the priorities in Washington, D.C., are,” he said on “Meet the Press.” “I refuse to even acknowledge the politics or the polling or the fear or the NRA. That has purchased the complicity and silence of members of Congress. And this weak response to a real tragedy in America, 40,000 gun deaths a year, we’ve got to do something about it.”

He along with two other Democratic presidential hopefuls, Sens. Cory A. Booker of New Jersey and Kamala D. Harris of California, have voiced support for mandatory buybacks.

Rather than push proposals like Mr. O’Rourke’s, most Democrats are focused on getting the Senate to take up their universal background checks legislation.

The bill in question would extend background checks to private sales between individuals — something that gravely concerns conservatives.

Sen. Ted Cruz said that option could be the start of a slippery slope that would lead to gun confiscation plans like Mr. O’Rourke’s.

“The only way to enforce that is a federal gun registry, and a gun registry is the step you need for gun confiscation,” he said on ABC’s “This Week.” “The federal government should not be confiscating guns from law-abiding citizens.”

While Republicans have meeting with the president to go over his options, Democrats have been pressuring him to intervene on the Senate’s stalemate, where Mr. McConnell is waiting to see what Mr. Trump is willing to support.

Speaking with the president on the phone Sunday, House Speaker Nancy Pelosi and Senate Minority Leader Charles E. Schumer said they offered to join him in a “historic signing ceremony” at the White House should it pass the Senate.

“This morning, we made it clear to the President that any proposal that does not include the House-passed universal background checks legislation will not get the job done,” they wrote. “We will not stop until these bills are passed and our children’s lives are safe. We call upon Senator McConnell to ‘Give Us a Vote!’”

According to the White House the conversation between party leaders was “cordial,” but the president made no commitments regarding the Democrats’ background-check bill.

Counselor Kellyanne Conway said Sunday that the president is considering a number of bills, including “lie and try” that cracks down on those who put misinformation on forms when trying to buy a gun. However, Mrs. Conway noted the president is concerned that some measures to extend background checks could be used as a cover to try and enact mandatory buybacks.

“We’re not going to allow bad actors who should not have firearms in the first place … to be the excuse that a bunch of liberals and socialists have to confiscate firearms from law-abiding citizens who has legally procured them,” she said on Fox News.

According to several Republican lawmakers meeting with the president on the issue, Mr. Trump is supportive of background checks generally but hasn’t made a firm decision yet.

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