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Mitt Romney and Newt Gingrich are embroiled in a war of words over "self-deportation," an idea the former Massachusetts governor proposed as a way to curb illegal immigration.

At first glance, the phrase appears contradictory. After all, how can a person banish themselves from a country?

Gingrich mocked the idea at a Univision forum Wednesday, saying it was based in fantasy and that his rival "shows no concern for the humanity of the people who are already here."

"I think you have to live in worlds of Swiss bank accounts and Cayman Island accounts and automatic $20 million-a-year income with no work to have some fantasy this far from reality," Gingrich said. "For Romney to believe that somebody's grandmother is going to be so cut off she is going to self-deport? This verges - this is an Obama-level fantasy."

But the concept itself is real and is rooted in the conservative idea of "attrition through enforcement," that would, in the words of its chief architect Mark Krikorian, "Shrink the illegal population through consistent, across-the-board enforcement of the immigration law."

The idea is that if laws and restrictions against undocumented residents are enforced more stringently, both at the federal and state level, then those immigrants would have no choice but to leave on their own.

A case in point is Arizona, which in April 2010 imposed the toughest crackdown of any state to curb the growth of illegal immigrants.

Another example is Alabama, where schools are now required to check their students' immigration status and law enforcement officials can arrest those who don't have paperwork.

"This strategy of attrition is not a pipe dream, or the idle imaginings of a policy wonk," Krikorian, executive director of the right-leaning Center for Immigration Studies, wrote in a 2005 report. "The central insight is that there is already significant churn in the illegal population, which can be used to speed the decline in overall numbers.

Over the years, the idea has gained traction among some conservative policymakers.  Reps. Lamar Smith, R-Texas, Elton Gallegly, R-Calif., and Steve King, R-Iowa, have all spoken in favor of the policy.

Liberals say the policy equates to mass deportation.

But Krikorian argues that all policies to curb immigration are essentially based on this idea of "self-deportation."

"We banned the employment of illegal immigrants, audited businesses hiring illegal immigrants - They were all based on this concept of self-deportation, so the administration is already following this strategy," he told ABC News. "It's just that they are doing it in a half-hearted way and they are negating it with other measures."

Whether such a policy would be successful in curbing illegal immigration remains to be seen. And it's too soon to gauge whether the recent crackdowns at the state-level have been effective.

In some cases, however, there have been unintended consequences. Arizona's 2007 law requiring employers to use E-Verify to check their workers' immigration status reduced the number of unauthorized employees by 17 percent from 2008 to 2009, but many of them went into self-employment rather than leave the state, according to a report by the Public Policy Institute of California.

Nationally, forceful removals have doubled in the last ten years - climbing to more than 387,000 in 2010, from 188,000 in 2001. But so-called "returns" have declined, dropping to 476,000 in 2010, half as many as in 2006, according to the Department of Homeland Security. Most of these voluntary returns were of Mexican nationals who had been apprehended by the U.S. Border Patrol and were returned to Mexico, DHS said.

Romney first suggested the idea of self-deportation at Monday night's NBC debate, when asked how he would propose sending back illegal immigrants, if not by deportation.

"The answer is self-deportation," he responded. "People who come here legally would be given a transition period to work here, but then they would no longer have the documentation to stay here. We'd have a card that says who is here legally. If they're not here legally, they're going to find they can't get work here. Ultimately, with this transition period, they would get in line at home."

Romney has hit back at Gingrich for criticizing the idea, citing an interview with conservative radio host Laura Ingraham, in which the former House speaker agreed with Ingraham's comments on enforcing the law and self-deportation, and another case in which Gingrich's spokesman R. C. Hammond said that "the vast majority of them would self-deport" if the border was secure and a more effective immigration policy was enforced.