The comment is often attributed to Hitler, who organized youth groups to introduce children to Nazi ideologies.
Illinois Republicans including U.S. Rep. Adam Kinzinger and state GOP Chairman Tim Schneider condemned the comments.
“That language is wrong and disgusting. We urge Congresswoman Miller to apologize,” Schneider said in a statement.
Illinois Gov. J.B. Pritzker, a Democrat who is Jewish, called the remarks “unfathomable.”
“Let me be clear: Hitler got nothing right,” he told reporters Wednesday. “This reprehensible rhetoric has no place in our politics.”
Miller, elected to public office for the first time, runs a farm with her husband, Republican state Rep. Chris Miller. Her congressional district covers a wide swath of southern and eastern Illinois along the border with Indiana.
Messages left Wednesday for spokeswomen for Miller and “Moms for America” weren’t returned.