This is the point I think most people here are missing/might not have experienced. In California for example, its almost guaranteed you will be at a CC for 4 years now before getting all the classes you need to graduate. Times are tough and not only are state budgets slashing funding to CCs, but more people than ever are returning to school. Basic Supply and Demand situation. Supply is low, demand is high which means you have a major gap in availability of limited resources.
In lab classes (lab classes being those like chem, bio, etc) the teacher has no say how many people can enroll, they are limited by the amount of people a lab can handle. From experience (I got out BEFORE all this budget **** went on), in non-lab-classes, the teachers will usually allow as many people as building safety codes allow people to be in a classroom (if they have the authority to do so, they may not).
Best thing to do is wait it out as long as you can, like others have said, there's a point at which the registrar won't allow anymore late adds, your hope is that someone drops before then, and be the next in line to get. I do not envy those going into CC's now. Read a post by me a few years ago, I was the first to come to the defense about the quality of education CC's provide, but with budget cuts, **** just got nasty!