Just to point out the obvious in case it wasn't. The problem is not children per se. It's the fact that children become adults. An adult not having children equals one adult's worth of impact. An adult having one child equals two adults' worth of impact. It's simple math.
Obviously, it also matters greatly whether the child who becomes an adult is an American or a Bangladeshian. (This is why countries have been postponing and squabling over the exact distribution of the necessary emission cuts for the past 25 years.)
The main question here is: how many people are currently alive?
A human being can go for 3 weeks without food. Therefore the number of human beings alive today (actually more like the weight of the total number of humans) is about equal to the previous month's food supply. [Civilization has no material food reserves.]
This food supply can be more or less wasteful. For example 17 pounds of grain equals 1 pound of meat equals ? pounds of human.
Obviously we can keep more people alive on grain than on meat.
The next issue is that currently it requires 1-2 persons + large amounts of fossil fuel inputs (tractors, fertilizer, ...) to feed 100 people. This is done somewhat inefficiently using practically all available agrarian land which top soil is being depleted rapidly (maybe a century left at current run off rates ... this will obviously change either voluntarily or forced).
A fully agrarian society will require close to 100 people working the fields to feed 100 people. Those among you who garden know how hard it is to replace your own food supply. The yields are much less. As far as I understand (big rule of thumb), standard agrarian methods are perhaps 1/6 as efficient as green revolution methods.
Since land [that can be used to grow food] is currently maxed out, this means that 100 people working the fields can feed a little over 17 people. Well, that is, only 17 of those will actually have to work. The other 83 have to go.
So the answer in terms of needing more children to work the fields using agrarian methods is an empathetic no!
Unfortunately, simple math goes against practically ALL foundations of human culture, religion, civilization, history, ...
Humankind has historically been an r-selected species. That is, as much offspring as possible, as fast a possible (start young), with as little effort as possible (don't invest). The goal of r-selected species is to take advantage of an abundant resource as fast as possible once it appears. Once it's gone, the r-selectors population crash but because there are now so many of them, a few will survive. Typical r-selected strategies are pursued by weeds, rabbits, businesses, religions(*), ... well basically most human institutions.
However, with mass-industrialization, there's been a tendency towards k-selection. K-selection favors a stable society: little offspring, slow growth (start older), using a lot of effort to build quality replacements. For example, as people get richer and more educated, they delay having children, the have fewer children, and they invest heavily in their children's education.
(*) This might interest you. Consider that the major monotheistic religions all derive from sheep herding communities. They are, therefore, propagating the values of having a sheep herder in charge of creating as many sheep as possible. The preferred strategy here obviously has to be r-selected. So major religious tenets of an religion that originated in animal care will be r-selected. Compare to agricultural religions which prefer a K-selected strategy. These tend to associate practically every thing in their world with its own god. The water god, the thunder god, the harvest god, .. We have few of those religions with any impact in today's world. Note. I point this out to illustrate how deep the foundation of religious beliefs tend to go.
Similarly, the dominant religion of the developed world: materialistic consumerism is r-selected. Practically all economics is based on r-selected theories: how to create the fastest growth while consuming an apparently abundant resource.
So here's the situation:
1) Humans have historically been r-selected but demonstrate some capacity for K-selected behavior. There's another kind of behaviour which is called eusocial behaviour. Eusocial is hardcore. I'm not even sure humans have the capacity for this. You (by which I mean 99.9% of the population) gotta be some kind of saint for that to work out. Well, humans do have saints, but few achieve that status.
2) Due to history, practically all human institutions and beliefs are r-selected.
3) Due to a spurious geological accident, we have been able to temporarily extend our population numbers to 6x of what we can otherwise hope to achieve.
Here are the barriers towards a non-standard solution, by which I mean one which doesn't involve the usual 4 resolutions of an r-selected species hitting capacity: pestilence, war, famine, and death.
1) As mentioned, humanity would have to find a technological miracle. This is obviously the preferred method since it is the easiest. "They will think of something". This is why we have notions such as "green tech", "sustainable tech", ... It's the idea that we can solve our growth barrier by growing more but in a different direction. Note how this requires little introspection.
2) Civilization will have to change practically ALL its major institutions and beliefs. How likely is it that a majority of humans will do the simple high school level math AND bring their behaviour in terms of economic beliefs, lifestyle beliefs, religious beliefs, political beliefs, etc. in accordance with that. I say not very many.
Possibly the biggest obstacle is democracy coupled with post modernism and the achievement of completely detachment from the reality of things by most people allowing the common acceptance "I disagree with the facts because they're not compatible with my political/religious/etc. beliefs" as a perfectly shameless and in most circles acceptable argument.
PS: If anyone wants to disagree with the facts because of their political/religious/etc. beliefs, we should probably start another thread. Before doing that please bang your head against the wall 10 times. I will do the same