After Republican presidential candidate Herman Cain told a campaign audience that he believed the federal government should erect a deadly, electrified, 20-foot border fence to help stem the flow of illegal immigration, one of the top Hispanic lawmakers in Congress slammed the GOP hopeful for “a staggering lack of sensitivity” and called on other candidates seeking the nomination to reject Cain’s proposal.

It began Saturday as Cain stumped in Cookeville, Tenn., where the surging candidate detailed his solution to the country’s illegal immigration trouble.

“First, secure the border for real,” Cain explained . “It’s common sense. Part of [the solution] would have a real fence. Twenty feet high, with barbed wire – electrified – with a sign on the other side that says it can kill you. It’ll be in English and Spanish.”

Those comments drew a sharp rebuke from Rep. Charles Gonzalez, the chairman of the Congressional Hispanic Caucus, who warned Cain against using his popularity to irresponsibly stoke public opinion.

“Words have consequences, both in shaping ideas and inspiring actions,” Gonzalez, D-Texas, wrote in a statement on Monday. “Whether or not he made his comments in jest, Mr. Cain’s words show a lack of understanding of the immigration issues our country is facing and a staggering lack of sensitivity. Surely, Mr. Cain understands the duty that candidates have to offer responsible policy proposals.”

Even before Gonzalez could react to the comments, Cain dismissed critics who believe his rhetoric is insensitive.

“Then I get criticized: ‘Mr. Cain, that’s insensitive,’” Cain said. “What do you mean insensitive? What’s insensitive is when they come to the United States across our border and kill our citizens and kill our border patrol people. That’s insensitive and I’m not worried about being insensitive to tell people to stop sneaking into America.”

Gonzalez, a 7-term lawmaker representing the San Antonio area, also called on the other Republican candidates to distance themselves from Cain’s commentary.

“Mr. Cain has said that America ‘needs to get a sense of humor,’ but I see nothing funny about killing other human beings. Leave the comic routines to the professional comedians,” Gonzalez stated. “The most pressing question is how the other Republican candidates respond to this ‘policy position’ by Mr. Cain. I urge these candidates to immediately repudiate Mr. Cain’s comments and to show strong disapproval of even so-called jokes about killing human beings.”

Gonzalez said that considering Cain’s past experience as an executive in the restaurant industry, a labor force that is 22 percent Hispanic, he and other members of the Hispanic caucus “hope [Cain] would follow the responsible path taken by the National Restaurant Association” in calling for comprehensive immigration reform.

ABC News’ Susan Archer contributed to this report