It's a pretty tough question to answer here.
On the one hand, I'd like the government to stay the hell out of people's bodies unless what they are doing directly effects someone else. A strong case can be made for abortion here, whether it's right or wrong, but I'm more/less on the side of your pro-choice folks up to a point.
What becomes difficult in figuring out whether this is a good idea or not is who gets to decide who can have children and by what criteria? If we have criterian based on socioeconomic status or how someone scores on an IQ test (note, I did not say actual intelligence), then I think we will have a disproportionate amount of minorities effected by this. On the other hand, an extension of affermative action as far as permission to procreate is something that I'd almost find to be humorous.
If someone far smarter than myself could come up with a fair system by which we could judge someone's suitability to procreate, then I'd be for it. However, I don't think such a system could really ever exist.
What China has done is an interesting variation of such a system. Each woman is only allowed to have one child. If they have a second, an abortion is forced. I don't think anyone, liberal, conservative, green or whatever thinks that system works very well (or is very fair).
I really don't see this as a liberal/conservative type of debate. I think this is an issue that people that identify with either end of the spectrum would be divided amongst themselves on. To oversimplify it in a liberal/conservative manner really doesn't do it justice.
Now, if we could just perfect a way to reproduce without actually involving the human body, that would solve all these problems completely