"We don't need weapons like that on the street," he said. "It's time for the NRA to step aside."
LaPierre and Hutchinson declined to take questions about their proposal, including whether the NRA is working with the White House. Obama this week asked Vice President Biden to head up efforts to address gun violence.
In recent years, Americans have struggled with the questions raised by horrifying mass acts of violence, including the 2007 Virginia Tech shooting and the 2011 Arizona shooting spree that killed six and wounded then-Rep. Gabrielle Giffords. But the age, innocence and vulnerability of the Newtown, Conn., children challenged even some strong advocates of gun rights to reconsider their position, particularly on military-style weapons and large-capacity magazines that allow shooters to fire multiple rounds.
"Everything should be on the table," West Virginia Sen. Joe Manchin, a conservative Democrat and lifelong NRA member, said earlier this week, although he later insisted, "I'm not supporting a ban on anything."
Giffords' husband, Mark Kelly, issued a statement Friday saying the NRA's proposal represents "extreme rhetoric" whose time was over.
"The NRA could have chosen to be a voice for the vast majority of its own members who want common sense, reasonable safeguards on deadly firearms," he said, "but instead, it chose to defend extreme pro-gun positions that aren't even popular among the law-abiding gun owners it represents."
Republican leaders were mostly silent after the LaPierre speech, with some unsurprising exceptions: Rep. Don Young, R-Alaska, an avid hunter and longtime gun-rights advocate, applauded the proposal.
"Schools across the country have become unnecessary targets to violence and mayhem," he said in a statement. "Having trained law enforcement within the school to protect both the staff and our children would provide a line of defense that has long been afforded various institutions, such as our nation's airports, federal buildings and museums."
School officials, including Education Secretary Arne Duncan, dismissed the NRA idea. Schools should be "safe sanctuaries, not armed fortresses," said Randi Weingarten, president of the American Federation of Teachers. New York City Mayor Michael Bloomberg, an independent who has led a national campaign to reduce gun violence in cities, called LaPierre's speech a "paranoid, dystopian vision of a more dangerous and violent America, where everyone is armed and no place is safe."
Some Republicans, such as New Jersey Gov. Chris Christie, also said schools shouldn't be "armed camps for kids."
"I don't think that's a positive example for children," he told reporters Friday during an event in Newark. "We should be able to figure out other ways to enhance safety."