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“America has to bite the bullet of what these incidents mean to our people, to our nation and our nation’s standing in the world,” she said.

Mr. Obama and lawmakers who favor gun control acknowledge how difficult their efforts will be. Any significant measures likely will require the support of at least some Republicans. Backing from the NRA, which thus far has opposed any new limits on firearms, also would go a long way in spurring Republicans and the public to support new legislation.

“This is going to be a sustained conversation over time as people think about this,” said Agriculture Secretary Tom Vilsack, speaking Sunday morning on CNN’s “State of the Union.”

“Conversations not just at the national level but conversations that engage people at the local level … it’s grass-roots up,” he said. “This could be a unifying conversation, and Lord knows we need to be unified.”