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Indeed, Mr. Obama and his allies in Congress plan to forge ahead.

Senate Majority Leader Harry Reid, Nevada Democrat, said last week that the national conversation on gun control is not over, though he has acknowledged that passing legislation in the current political climate is a long shot.

Over the weekend, Mr. Bloomberg promised that “our fight to end this dreadful national tragedy will go on. Mark Kelly, husband of former Rep. Gabrielle Giffords, herself wounded during a shooting in Tucson, Ariz., in 2011, said that he and his organization, Americans for Responsible Solutions, will be part of the debate “for the long haul.”

Again using his unique pulpit as commander in chief, Mr. Obama took the same position Saturday before he and first lady Michelle Obama took part in a moment of silence and candlelighting ceremony to honor the Sandy Hook victims.

“On this anniversary of a day we will never forget … we haven’t yet done enough to make our communities and our country safer. We have to do more to keep dangerous people from getting their hands on a gun so easily. We have to do more to heal troubled minds,” Mr. Obama said.

The president’s mention of the need to “heal troubled minds” underscores a subtle yet important development in the larger debate. Over the past year, the national conversation, while still focused on gun control, has begun to shift to the need for greater mental health services.

Gunmen such as Lanza, the Navy Yard shooter Aaron Alexis and others have exhibited clear signs of mental illness. Despite disagreements on gun control, there is a widespread consensus that firearms must be kept out of the hands of the mentally ill.

Similarly, there is agreement on the need for greater services to address the mental health issues that sometimes lead directly to violence.

Last week, Mr. Biden — after meeting with families of victims of the Newtown shootings — announced $100 million in additional federal funding for mental health services across the nation, including $50 million specifically to construct or expand facilities in rural areas.

But even that effort is just a drop in the bucket, say professionals, who believe the scope of the mental health problem isn’t fully understood by political leaders or by the American population as a whole.

“We need a lot more spending and treatment on early intervention,” said Jamison Monroe, the founder and CEO of the Newport Academy, a mental health treatment facility 30 miles from Sandy Hook.

Mr. Monroe said the announcement of more federal funding “is a sign that the administration recognizes this is an area of concern and that an investment in this area will help improve life for a number of individuals and hopefully prevent tragedies from happening.”