I agree with your view on the types of responses to the discussion of overpopulation, and I will elaborate them using some examples of possible "solutions".
To the problem of a growing population/(impending) overpopulation there are 2 types of solutions:
Type 1 - Adapt to the new situation, provide for the growing population.
Type 2 - Prevent population growth.
Regarding type 1:
If we are to even attempt to provide for the growing population, we will have to make some drastic changes or we are going to run out of resources. The first resource, endangered by the growth of our population, that comes to mind is food: although intensifying agriculture and perhaps methods such as genetically enhanced crops are possible, these measure are often met with critisizm. The second "resource" that comes to mind is space will need to be able to use our space more efficiently if our population is to continue growing, as space is gonna be a major factor in the possibility to continue growing our population (space to live, space to grow crops, space to produce energy, etc.). I will concentrate on these two.
Firstly, food. It is obvious that in the future, with a continuously growing population, we will have to heighten our food production to be able to feed everyone. One possibility through which our future food problems may be postponed is the intensification of agriculture. However, the general response to intensifying agriculture, in particular the use of domestic animals, is "oh the poor pigs/chickens/cows/etc, animal rights blah blah blah!" when they are packed against each other in "too small" housing. The pork appartments are not something the majority of people would condone after their attention has been raised to the issue. Intensifying the farming of crops may lead to disastrous consequences for the soil when not done properly.
Plus these measures will oftenly mean the doom for small farmers as they can't compete with the big companies/farmer unions.
As our Western population is not growing in number (some countries even having negative population growths), this is not going to affect us directly. However, Asian, African and Middle-/South-American countries are definitely gonna feel the consequences of their growing populations (especially countries like India, where they breed like bunnies). Sadly, these are exactly the countries where it will be difficult to intensify agriculture, because of their numbers of small farmers who do not have the money to afford the necessary equipment to intensify their production. Companies that are able to intensify, when regulations allow, will ruin small farmers in competition (worse than now as most countries have at least some form of regulation in agriculture, for instance protection of small farmers and prevention of international companies to set up farms to a certain extend, which obviously would have to be discontinued to allow for intensification.) Either intensification in these countries will lead to the disappearance of small farmers (and huge increases in unemployment rates), or they will be a complete failure.
The discussion on genetically enhanced crops is one that has been held many times before, so I will skip this as it generally doesn't end in anything productive. (not that most discussions on these forums do, but I'm just too lazy to state what's been said many times before 
).
Secondly, the issue of space. Space is bound to run out when more people need housing, more space is required for production of energy (think windmill parks, but traditional electricity-producing (through means of burning fossil fuels) facilities as well). Same goes for the production of food, unless intensified.
The obvious solutions to these problems (condominiums, nuclear power plants or other powerplants that produce a relatively large amount of energy on small amounts of space, and the intensification of agriculture) are generally disliked by the majority of the population.
An alternative way of intensifying food production is by use of vertical farms. However, these vertical farms would be quite expensive and only affordable to the richer of countries, in which, as stated before, overpopulation will not be as drastic.
Regarding Type 2:
Preventing population growth is nearly impossible. Impossible, because in modern democracies people have the right for themselves to choose whether to reproduce and whatnot, nearly because in totalitarian societies or governing systems that provide more control over the population, you can limit personal freedoms and ensure the population will not grow. China's (attempt at a) one child policy is an example of this. However, the thought that these changes will be implemented in other countries is unrealistic, since it requires a strong government with ways of enforcing laws on the people to ensure that people will obey such a law. However, the ways of enforcing laws, such as a strong (government obedient) army or effective propaganda, are often not developed enough in the countries that will be hit the hardest by overpopulation, as their governments tend to be weak and lack power (Africa, India).
Another possibility is to just let people with less access to resources die. However, this "solution" is generally frowned upon.
A key phrase in all of these "solutions" is "people dislike the solutions". Morale arguments form a major blockade against every attempt to combat overpopulation. Why? Because you are taking away some of their rights or rights of animals (some people, strangely, believe animals should have rights. Amazing!), for instance the right to reproduce (when limiting population growth) or to personal space (personal space is limited in condominiums) or those of animals (in the case of pork apartements).
It will either be a case of taking away peoples' rights in order to sustain the population, or having the population correct its own size through natural means. Either way people are going to complain.
My own point on the subject:
For those who haven't noticed yet I stand indifferent to many of the morale arguments people have against intensification of agriculture and other measures to save space. I believe a few adaptions to human rights are necessary to combat overpopulation, not only intensification in agriculture and higher space efficiency in housing, but also "mild" population size control measures such as a one child policy. If these measures are not made, we may face far more serious consequences and so I think they are an acceptable evil.
. In rural areas (and to stop parents only having males) they allowed parents to have a 2nd child if their first was a female. Also anyone from an ethnic minority is also able to have 2 children in order to maintain cultural lineage. The Chinese government is also considering extending the 2nd child policy (if the first is female) to urban areas (http://english.people.com.cn/90001/9077