"When I'm in charge of the fence, we going to have a fence. It's going to be 20 feet high. It's going to have barbed wire on the top. It's going to be electrocuted, electrified," Cain said. "And there's going to be a sign on the other side that says it will kill you."

But asked about the proposal Sunday on "Meet the Press," Cain said he was joking.

"That's not a serious plan, that's a joke," Cain said. "I've also said America needs to get a sense of humor. That was a joke, OK?"

Cain went on to say that he would actually secure the border through a combination of a physical fence, technology and possibly the presence of military troops.

But Gonzalez said the idea was no joking matter.

“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 said.

He went on to urge Republican candidates to "immediately repudiate Mr. Cain’s comments and to show strong disapproval of even so-called jokes about killing human beings.”

Minnesota Rep. and fellow White House contender Michele BachmannMichele Marie BachmannBoehner says he voted for Trump, didn't push back on election claims because he's retired Boehner: Trump 'stepped all over their loyalty' by lying to followers Boehner finally calls it as he sees it MORE, speaking at an event in Arizona, said that while she supported building a fence, she believed that immigration policy was not something that Cain should be joking about.

"This is no laughing matter, the border fence," Bachmann said. "We've seen jokes made by presidential candidates about the fence. It is not a joke. This is a real issue, and this is a serious issue."