Rather a large number of people are convinced of two things: that "overpopulation" exists as a concept, and that the earth is, or soon will be, overpopulated. I'll address these points separately.
Earlier, I have argued that there is no such thing as "the environment". I also don't think there is any such thing as "overpopulation". I believe that overpopulation is a confusing name for a bundle of ideas. When you look at the negative attributes of overpopulation, you will see that not a one of them is actually inherent in having a large number of people. The confusion in calling this set of problems overpopulation is that it asks and answers the question. It says "The solution to these problems is to control population growth."
Google found a list of problems that some Carleton College students listed. They seem a reasonable-enough list: More cars (more pollution), direct effect on the water table, overuse of natural resources, deforestation, urban sprawl, clearing land for residential use, increased air pollution, increased garbage, overuse of fossil fuels and global warming.
There's not a one of them that is necessarily corrected by having fewer people. For example, if there are fewer people and hence fewer cars, there would be less congestion on the roads. People would find it easier to drive. With fewer people, you have a smaller "mass" to satisfy your mass transit. So busses and trains would have a smaller market. Fewer people might just as well end up causing more miles to be driven rather than fewer.
People do not necessarily need to clear land for residential use. Look at the Northeast, where the population has grown AND the forests have grown.
I'm not going to say that the problems commonly lumped together as overpopulation are not problems. They are problems. Attempts to make fewer people are not necessarily going to fix those problems. Attempts to fix the problems are more likely to fix the problems. Now, if you define as a problem your opinion that there are "too many" people, then you should be subjected to this test: Pick the people you think shouldn't exist. If you think America is currently doubly overpopulated (and some people do), then you should be happy if I chose at random half of your friends for you to give up. You have to tell these (soon to be former) friends "I wish you didn't exist. The world would be a better place without you. Never speak to me again."
Free-market economies naturally grow. Every trade makes everyone better-off, and since people are free to trade as much as they wish, free-market economies grow in value faster than any other type of economy. Since the economy becomes more and more productive, more and more people are needed to work. Population growth needs to be seen as something that doesn't necessarily make us poorer. Depending on the corresponding growth of the economy, a low population growth rate might actually make us worse off, as businesses have to do less because they can't find workers.