Republican presidential candidate Newt Gingrich explained on Sunday that his policies would require up to 9 million undocumented immigrants to return to their home nations -- and he predicted that they would do it voluntarily.

"What I've proposed is very standard things," the former House speaker told CBS host Bob Schieffer. "In that context, what I've said is there is a group of people that have been here for a long time, and we've talked about a citizen review board in the World War II Selective Service model, and we've said that if somebody's been here a long time and has an American family willing to sponsor them, they should be subject to review to get a residency permit -- not citizenship, but a residency permit."

He continued: "I just disagree with some of my [Republican] friends. I do not believe the American people are going to send police out to round up folks who have been here 25 years."

"There are 11 million of these people," Schieffer noted. "I mean, what are you going to do with them?"

"My guess is that 7 or 8 or 9 million of them would ultimately go home, get a guest-worker permit, come back under the law," Gingrich replied. "But the last million or 2 are people that have been here for a very long time. They're very part of -- they're not citizens, but they're part of the community."

"One of the requirements would be that they would have to have an American family sponsor them to be eligible for review by the citizen review board. I think it's a responsible position that recognizes the humanity of the problem, but firmly establishes the rule of law," the candidate added.

GOP hopeful Mitt Romney, who has called Gingrich's plan a form of amnesty, has also said undocumented immigrants would have to return to their home countries before applying for citizenship.

“For those that have come here illegally, they might have a transition time to allow them to set they affairs in order, and then go back home and get in line with everybody else,” Romney told supporters in Cedar Rapids, Iowa earlier this month. “They start in the back of the line, not at the front of the line.”

Watch this video from CBS's Face the Nation, broadcast Dec. 18, 2011.