Shortly after the Newtown shooting, LaPierre also called for armed security guards in schools.
A 20-year-old gunman killed 26 students and educators and himself at Sandy Hook on Dec. 14, after having shot his mother to death at their Newtown home.
Another Newtown resident, Christopher Wenis, told The Huffington Post that he received three of the NRA's robocalls last week.
"I've got a 5-year-old son who went to preschool on the Sandy Hook Elementary School campus," Wenis said. "And this was a really hard week for me on a lot of levels. These calls were the very last thing I needed."