WASHINGTON — The National Rifle Association provoked a furious response from the White House on Wednesday by releasing a video accusing President Obama of being an “elitist” and a “hypocrite” because he opposes posting armed guards at schools, while his daughters have Secret Service protection.

The video also prompted commentary on social media about whether the gun rights organization might have been too strident, even for its own members.

The White House lashed out at the N.R.A. even as Mr. Obama stood with young children to unveil broad proposals to create tougher gun laws and use the power of the presidency to keep guns out of the hands of criminals.

“Most Americans agree that a president’s children should not be used as pawns in a political fight,” said Jay Carney, the White House press secretary. “But to go so far as to make the safety of the president’s children the subject of an attack ad is repugnant and cowardly.”