Newtown, Conn., Superindent of Schools Janet Robinson on Wednesday blasted critics who suggested armed teachers would have stopped the Sandy Hook Elementary School shooting.

Robinson, speaking on Capitol Hill during a House hearing on gun violence, said she felt remarks made in the wake of the shooting suggesting that Principal Dawn Hochsprung could have killed the shooter had she been armed were "insensitive." Robinson said, "She wasn’t at her desk and no good principal is."

Robinson flat-out rejected the NRA proposal to place armed guards in every classroom in America, noting that the weapon used in the Sandy Hook shooting was a semi-automatic. "They didn't have a chance," she said.

And she added that she doesn't envision elementary school teachers "packing" weapons while they sit on the carpet with small children—children who she said could be at risk around inexperienced gun owners.

Robinson called on Congress to help offer long-term support to her community. "Mental health is a big piece when you have lost your whole sense of safety," she said, noting that Newtown residents want concrete signs of safety including a visible police presence.

The hearing, hosted by House Democrats, was designed to gather input on how to combat gun violence. Though Congress was out of session, the event drew more than 60 members from both parties to a standing-room-only venue that required an overflow room.

Earlier on Tuesday, President Barack Obama, standing beside Vice President Joe Biden, had unveiled a sweeping plan to combat gun violence.