Just in case you had any thoughts about just how far the GOP base has shifted into insanity, I offer this as proof that they are currently hopelessly lost. Then, I offer this rebuttal as a starting point for this particular discussion.
First and foremost, let's address this idea regarding child labor. For the last century or so, children have been kept out of factories, mines, and other dangerous or inappropriate work places by laws that limit how old a person can be to have a job. Children are not allowed to work anywhere full-time. In fact, the only thing that children seem to be able to do to make a living these days is work on the family farm or open a lemonade stand.
The reason for this is that America realized that it has a heart and a soul, and that those things were contingent upon how well it treated its citizens. It may have been good for business to have cheap, youthful laborers who can crawl into small spaces to fix or retrieve things, but it's not moral or ethical. We stopped forcing children to take on work because it was hazardous to their health and their future.
Apparently, Gingrich does not understand this, or he would not have proposed this idea. As the first link above indicates, Gingrich suggested firing unionized janitors at schools (how many jobs would that cost?) and instead offering the poorer students the chance to do the work themselves. While Gingrich tries to make this a lesson in civic duty and taking pride in one's school, he misses the rather large point that this is not what schools are for, and not what poor students should have to do.
Education is a free right in this country. We have laws that say children must attend school for a certain number of years, and that education is not something that should be based on your ability to pay for it. But that's what Gingrich's mentality pushes us towards. I've said it many times in my critiques of charter schools and the privatization of education: for-profit education, or any other fleecing of the American Poor such as this, is frankly un-American. We are better than this, and Gingrich should know better.