Newt Gingrich spoke in Arizona, criticizing the Obama administration for their lawsuit against Arizona, saying “There is something truly absurd about a federal government that refuses to control the border, refuses to do its job, and then attacks a local state."
"My stand is that we should have absolute control over the border," Gingrich said. "We should have English as the official language of government." Although unlike many of his Republican counterparts, Gingrich has a positive plan for citizens here illegally. He wants to modernize the deportation laws
"[Illegal immigrants] should pay a penalty, but they should then get a Red Card which would not put them on the road for citizenship, but it would bring them in from illegality," he said. [Emphasis added]"It would make them part of the community, and their children and grandchildren could aspire to become American citizens."
[Newt Gingrich talks Arizona immigration,  By Steve Kusj, abc15.com, October 20, 2011]
This is either very cynical, or completely misses the point.
The Red Card plan--legalization with no chance of citizenship--means employers would be able to hire cheap, formerly illegal labor, but Republican legislators would not suddenly have a bunch of Democratic voters added to their districts. That means that Republican legislators are the only Americans whose jobs would be protected by that plan. Might be a little easier to get through the House!
Alternatively, Gingrich is completely missing the point of illegal immigration. (I actually favor this over cynicism--Gingrich is a big point-misser.)
They want to live in America,  and earn American dollars. If Gingrich gives them that, he can keep the citizenship papers.
As for the part about their "children and grandchildren could aspire to become American citizens," well, under current law , their children if born in the US, and grandchildren, who will definitely be born in the US, will automatically be American citizens, anyway, because Gingrich couldn't be bothered to deport their parents.