Rep. Jerrold Nadler, D-N.Y., called the NRA's response "both ludicrous and insulting" and pointed out that armed personnel at Columbine High School and Fort Hood could not stop mass shootings. The liberal group CREDO, which organized an anti-NRA protest on Capitol Hill, called LaPierre's speech "bizarre and quite frankly paranoid."
"This must be a wake-up call even to the NRA's own members that the NRA's Washington lobbyists need to stand down and let Congress pass sensible gun control laws now," CREDO political director Becky Bond said in a statement.
The NRA's proposal would be unworkable given the huge numbers of officers needed, said the president of the International Association of Chiefs of Police, Craig Steckler.
He pointed to budget cuts and hiring freezes and noted that in his hometown of Fremont, Calif., it would take half the city's police force to post one officer at each of the city's 43 schools.
The Department of Education has counted 98,817 public schools in the United States and an additional 33,366 private schools.
There already are an estimated 10,000 school resource officers, most of them armed and employed by local police departments, in the nation's schools, according to Mo Canady, executive director of the National Association of School Resource Officers.
Gun rights advocates on Capitol Hill had no immediate comment. They will have to walk a tough road between pressure from the powerful NRA, backed by an army of passionate supporters, and outrage over the Sandy Hook deaths that has already swayed some in Congress to adjust their public views.
A CNN/ORC poll taken this week found 52 percent of Americans favor major restrictions on guns or making all guns illegal. Forty-six percent of people questioned said government and society can take action to prevent future gun violence, up 13 percentage points from two years ago in the wake of the shooting in Tucson, Ariz., that killed six and wounded then Rep. Gabrielle Giffords.
Since the Connecticut slayings, President Obama has demanded action against U.S. gun violence and has called on the NRA to join the effort. Moving quickly after several congressional gun-rights supporters said they would consider new legislation to control firearms, the president said this week he wants proposals that he can take to Congress next month.
Obama has already asked Congress to reinstate an assault weapons ban that expired in 2004 and to pass legislation that would stop people from purchasing firearms from private sellers without background checks. Obama also has indicated he wants Congress to pursue the possibility of limiting high-capacity firearms magazines.
Sen. Dianne Feinstein, D-Calif., said former President Bill Clinton called her with an offer to help get an assault weapons ban reinstated. Clinton signed such a ban into law in 1994, but it expired after 10 years.
Feinstein said she's not opposed to having armed guards at schools, but she called the NRA proposal a distraction from what she said was the real problem: "easy access to these killing machines" that are far "more powerful and lethal" than the guns that were banned under the old law.
Associated Press writers Andrew DeMillo in Little Rock, Ark., and Alicia A. Caldwell in Washington contributed to this report.