Illegal immigration questions at an early GOP debate Wednesday night riled up some of the lower-polling Republican presidential candidates -- particularly Louisiana Gov. Bobby Jindal, who contested CNN moderators' suggestion that he supported amnesty for illegal immigrants.

Jindal, whose campaign has struggled to get off the ground, maintained that he does not support amnesty and never has. Instead, he said the border needs to be secured and that a pathway to citizenship needs to include programs to assimilate immigrants. "Immigration without assimilation is invasion," Jindal said. 

Jindal cited the example of his parents, who immigrated to the United States 45 years ago from India. "They adopted the values," he said. "They did not come here to be hyphenated Americans."

Jindal said he opposes the sanctuary cities that provide shelter to illegal immigrants and would arrest lawmakers in the area.. "We do need to jail those mayors and councilmen as accessories for crimes," he said.

Former Pennsylvania Sen. Rick Santorum, who does not support amnesty, challenged Jindal's views. He said his own policy is in the best interest of "hard working Americans." "The reason we see this issue taking off is because workers in Americans know that their wages are being undermined," Santorum said. 

Former New York Gov. George Pataki held an opposing position from the other candidates on stage, advocating for citizenship for U.S-born children of illegal immigrants. "We can't just ignore them, or send them back," Pataki said.

Jindal, Santorum and Pataki were invited to the early debate held for the lower-polling candidates at 6 p.m. South Carolina Sen. Lindsey Graham also joined them on stage.

Although they were knocked out of the prime-time spot, the four candidates may be afforded more exposure than their more popular rivals. Since the stage is sparse, they received more airtime than their opponents on the main stage. Top-tier candidates will only have one minute to answer questions at the 8 p.m. debate, according to CNN rules.

Pataki, Graham and Jindal received less than 1 percent of support from Republican primary voters in Tuesday's New York Times/CBS News poll. Santorum was in the lead of the pack with 1 percent of the votes across the field.

The lower-tier debate was held in Simi Valley, California. Moderated by CNN, the debate aired at 6 p.m. Wednesday.

A second, prime-time debate was scheduled for the 11 top polling candidates at 8 P.M. EDT, also on the network. It will feature the top-polling candidates: New Jersey Gov. Chris Christie; Ohio Gov. John Kasich; billionaire businessman Donald Trump; former Florida Gov. Jeb Bush; Wisconsin Gov. Scott Walker; retired neurosurgeon Ben Carson; former Arkansas Gov. Mike Huckabee; Texas Sen. Ted Cruz; Florida Sen. Marco Rubio, Hewlett-Packard CEO Carly Fiorina and Kentucky Sen. Rand Paul.