“There is more Republican interest and involvement today than any time since Sandy Hook,” Mr. Murphy said. “So by definition, that’s different, right? But I also have failed every single time. Almost without exception, these talks, when they start, don’t go anywhere, right? And so I worry about claiming optimism, given that history.”…

Mr. Murphy said he spoke to members of Mr. Biden’s White House staff on Friday, who told him the president was eager to do anything he could to support the nascent negotiations over new gun safety measures.

“He can’t be hands off and he won’t be hands off,” Mr. Murphy predicted, adding, “I think you’ll see him being actively involved over the weekend and into next week.”

But the president and his aides remain wary. There is little appetite for Mr. Biden to pledge action that he knows will fail, setting himself up to look politically impotent. Aides also have cautioned that too much involvement by the president could further politicize the debate, making it harder for Republicans and Democrats on Capitol Hill to reach consensus. And forcing moderate Democrats to take a symbolic, tough-on-guns stand could cost the party even more seats in the midterm elections this fall.