Encourage adoption. Government can put a bit more money into orphanages, so they can advertise a bit better. Sure, its not a long term solution, but I feel that if adoption were encouraged more, there'd be a bit lower birth rate (not by much, but still noticeable), and maybe a few less people on the streets.
How to deal with it on a large scale... Unfortunately, medicine is here to stay, which has increased human lifespan greatly. Medicine has also greatly decreased the death of children, meaning that they all grow up and consume resources.
I think really, the only way we can deal with this besides war, self imposed genocides, or restriction of human rights is technology. If we run out of a resource, we'll have to use something else to replace it, and hopefully, technology will be able to do that