A day after President Obama pledged to protect America's children and avert mass shootings like the one last week at a Connecticut elementary school, the White House on Monday provided no details about how Obama plans to reverse the tide of violence.

Gun-control advocates were encouraged by the president's pledge on Sunday to use "whatever power this office holds" to address the kind of gun-related violence that claimed the lives of 20 children at Sandy Hook Elementary School. But when pressed for specifics Monday, White House spokesman Jay Carney said only that the president's plan to combat gun violence would go beyond new restrictions on gun ownership.

"It's a complex problem that will require a complex solution," Carney said. "I don't have a specific agenda to point you to today."

The White House reiterated Obama's support of a federal assault weapons ban that expired in 2004 but declined to say whether the president would support instituting a new ban, as Sen. Dianne Feinstein, D-Calif., proposed, or appointing a national commission to study violence as Sen. Joe Lieberman, I-Conn., suggested.

In addition to an assault weapons ban, the White House could push to expand the use of criminal background checks for gun buyers. Obama could also make a push to beef up funding for mental health, according to officials familiar with the administration's discussions.

The deliberative pace Obama is taking on gun control is a familiar one for him, though analysts said public outrage over the mass murder of schoolchildren could force him to move faster.

"My perception of President Obama is that he frequently will hold back, get a lot of perspectives -- and I know that's frustrated people," said Kristin Goss, a political scientist at Duke University and author of "Disarmed: The Missing Movement for Gun Control in America." But pushing gun-control legislation through a Republican-controlled House will be a daunting task, she said.

Still, Sandy Hook Elementary School was the fourth mass shooting of Obama's presidency, and gun-control advocates said he needs to offer concrete proof of his commitment to fighting gun violence.

"I don't expect him to release a full plan already," said one prominent gun-control activist. "But c'mon, at least attach your name to something, anything. It would be a sign of good faith."

One encouraging sign for the president is the movement of several pro-gun Democrats - including Sens. Mark Warner of Virginia and Joe Manchin of West Virginia -- who now say they would support restricting assault weapons. Manchin's about-face was particularly noteworthy since he once ran a campaign ad in which he fired a rifle at an environmental bill.

"The Manchin statement was stunning; there's been a sea change," said Ladd Everitt, spokesman for the Coalition to Stop Gun Violence. "I'm not concerned about Obama yet. He wouldn't have put himself in that position [on Sunday night] if he didn't intend to do anything."

The debate over America's gun culture comes as Obama devotes extensive energy to avoiding the so-called fiscal cliff, but some on Monday said the political juggling act was no excuse for inaction.

"If Congress and the president can't focus on two things at once," New York City Mayor Michael Bloomberg said, "who on Earth did we elect?"