Former Pennsylvania Sen. Rick Santorum vowed to return 6 million undocumented immigrants to Mexico and Central America and bring back American jobs Thursday night during the Republican undercard debate for the least favorite candidates. Santorum said people in the United States illegally and other immigrants are hurting American workers.

"That’s why wages are flat-lined," said Santorum, a frequent critic of illegal immigration. He wasn't exactly making a brave declaration. Linking immigrants to troubling economic data is a popular point for many Republicans, who have long blamed undocumented immigrants for the woes of working-class Americans.

But numerous studies show undocumented immigrants aren’t stealing jobs – they are helping to expand the economy. “In the ongoing debate on immigration, there is broad agreement among academic economists that it has a small but positive impact on the wages of native-born workers overall: although new immigrant workers add to the labor supply, they also consume goods and services, which creates more jobs,” Heidi Shierholz, chief economist to the U.S. Department of Labor and formerly of the liberal Economic Policy Institute, wrote in a study funded in part by U.S. labor unions.

Meanwhile, David Griswold, former director of the Center for Trade Policy Studies at the libertarian Cato Institute, wrote: “The addition of low-skilled immigrants expands the size of the overall economy, creating higher-wage openings for managers, craftsmen, accountants and the like. The net result is a greater financial reward and relatively more opportunities for those Americans who finish high school.”

Santorum is right that wages have been flat for decades. "Today’s average hourly wage has just about the same purchasing power as it did in 1979, following a long slide in the 1980s and early 1990s and bumpy, inconsistent growth since then. In fact, in real terms the average wage peaked more than 40 years ago: The $4.03-an-hour rate recorded in January 1973 has the same purchasing power as $22.41 would today," the Pew Research Center noted in 2014.

The Fox Business-hosted debates in South Carolina came days after President Barack Obama gave his final State of the Union address Tuesday night, urging America to elect a successor that represents the best of America in a speech full of obvious jabs at Republican presidential candidates who have railed against illegal immigration, Syrian refugees, civil rights for Muslims and food stamps for the poor.

Former HP CEO Carly Fiorina and former Arkansas Gov. Mike Huckabee also debated issues including national security and the economy during the so-called kids table debate. Sen. Rand Paul of Kentucky refused to participate in the less-viewed forum after he was denied a post in the main event because of his low polling numbers. He told the Washington Post he would "take the debate to Iowa and New Hampshire" instead. The two states hold the nation's first presidential contests in a few weeks.

"I'm not willing to accept a designation as a minor campaign. We've raised $25 million. We've gotten on the ballot on every state. It's kind of ridiculous to arbitrarily rate the campaigns based on national polling," Paul said.

Thursday's undercard began at 6 p.m. ET and the main debate was scheduled to start at 9. Candidates invited to take part in the prime time event had the best polling averages in the most recent national polls, and were polling in the top five in Iowa or New Hampshire. The candidates who made the cut were billionaire business mogul Donald Trump; Texas Sen. Ted Cruz; Florida Sen. Marco Rubio; retired neurosurgeon Ben Carson; New Jersey Gov. Chris Christie; former Florida Gov. Jeb Bush; and Ohio Gov. John Kasich.