Sorry, but the U.S. government already has fubared family law in this country beyond recognition. For example, divorced fathers get such a raw deal I'm surprised they haven't joined the Occupy movements en masse with Molotov cocktails in one hand and Kalishnikovs in the other. Yes, it's that bad. I knew a guy a couple jobs back who had his driver's license taken away because he couldn't pay $600 a month in child support to his crackhead of an ex-wife. He's ex-Special Forces too, so if he ever goes off the deep end and decides to settle accounts with the State, I'll just grab a bag of popcorn because it'll be quite the scene.
Trust me when I say that making parents get a license from the U.S. government or state government would turn into a first-class clusterfuck, and that right quickly. I'm not saying that to be a jerk or to impugn the motives of the OP and Co. who have the idea--as with Marxism, decent-minded people can come up with some pretty serviceable arguments why licensing parents is a good idea. We've all seen enough jag-offs mis-raising their kids to think "there oughta be a law" at one point or another--likely several points. It's an understandable sentiment, especially when you've been jabbed in the knee for the third time by some spoiled brat in the supermarket check-out lane whose parent is obliviously jabbering away on a cell phone.
However, good sentiments often make bad policy, and this is one such time.
For starters, this idea would require a huge, new, invasive bureaucracy to enforce. Think the DMV is bad? The Bureau of Reproductive Licensing would be an order of magnitude worse. Funding? We're already living in an era when over 1 out of every 4 dollars the federal government spends is borrowed, and state governments are slashing everything from highway maintenance to schools to welfare to balance their budgets. Where would the money for this come from? Charging fees for a parenting license? That would open up an epic can of worms. Believe me when I say you don't want to go there.
Second, we live in a country where a significant percentage of the population actually believes government-assisted health care is some communist conspiracy to destroy America. I can guarantee you a parental licensing scheme would bring the tinfoil-hatters, militias, white racial chauvinists and fundies out in force. To quote a movie title, "There Will Be Blood." A couple posts back, someone said that this is irrelevant to whether or not parental licenses are a good idea, but I disagree emphatically. When a policy would be so hated by such a significant percentage of the population that we would see regular, ongoing incidents of social violence from arson to assassinations to truck bombs from sea to shining sea, that has to be involved in the decision-making calculus for the Powers That Be. That reality cannot be ignored. Telling naysayers "let them eat cake" doesn't turn out very well. We're seeing this right now in Greece, where bankers and government planners are in ivory towers doing what looks great on paper while hungry mobs gather and their country teeters on the edge of collapse.
Third, we would see corruption on a scale unheard of since Prohibition and Tammany Hall, if not longer. People would beg, bribe, and fake their way around this. I'd be shocked if a cottage industry worth billions, even tens of billions, didn't arise in a few short years, catering to would-be parents who wanted to expunge or remove whatever it was in their records preventing them from getting a license. The rich would buy their way past this. As for the rest...
Fourth, quite a few people would simply drop off the grid entirely to get around this. We'd see poor kids (because, after all, it would be the poor who would bear the brunt of this, I don't care what anyone says, that's how it would turn out in the real world), raised in secret in the backwoods and wilderness across the land. Hundreds of thousands of kids with no access to health care, education, or other social services. Look at the experience of undocumented aliens in America today for an idea...only more would be in this new underclass of "undesirables."
This is definitely not a road I want to see America travel down.