I probably shouldn't post to this topic, but I feel compelled to.
Unquestionably, stray cats are an issue in most parts of our country. Also, keep in mind that the government cannot possibly afford to take care of the problem without collecting enough taxes to support a proper shelter, even if it is simply a place to have them euthanized and properly disposed of.
Instead, if you can, support whatever local humane groups are in your area that already are doing absolutely everything in their power to help control the population with taking strays as the have space to do so (which is infrequent in most cases because the economy has reduced adoptions severely while increasing owner surrenders and outright dumping substantially). Unless they have a direct contract with local government to provide animal control service, humane groups generally receive no government money to operate with, and are 100% reliant on donations or an occasional grant that big groups sometimes get, but the grants are rare, and there are fewer overall right now due to the economy as well.
The action of catching, altering (spaying or neutering), and releasing strays may not sound like a good idea, but it actually eventually helps reduce the population in a given area because reproduction is reduced while the consumption of available food and rodents continues, which stops additional cats from wanting to move into a given area, and if continued consistently by enough people, the likelihood of additional cats moving back into an area once that population begins to die off lessens over time.
I recognize that for many, humane groups are considered to be populated with people who have little grasp on reality (in essence they think everybody involved are like the PETA people who give animal rescue a bad name because of their extremist views), and animals are just animals.
Also, in many areas, there is a far more pressing need in helping people right now than animals, again due to the economy. I understand and agree with that, and many others involved in animal rescue recognize that, too, yet many of us continue to try to help animals anyway because they respect the fact that, unless they are feral (wild), the animals are 100% dependent on people for their survival, and strays are often people's former pets, many of which simply having been turned loose due to the misfortunes faced by their former families.
In some areas, Mother Nature simply takes its course and increases the population of cat predators until the problem is naturally reduced, but I also recognize that those predators also prey on other types of animals that may be more desirable, thereby requiring landowners to take action themselves to protect their livestock and other interests in a cost effective manner, often by removing the excess cats and the predators using whatever means they choose, while maintaining a small population of cats to provide rodent control.
Everyone's situation is unique, and there are different solutions of varying effectiveness, and I am not actually here to judge, despite it probably seeming like that. I just wanted to provide a little different perspective with respect to this issue, due to my wife's involvement in animal rescue in Indiana, and by extension, my own. It is primarily a thankless, yet occasionally highly rewarding, effort that could use a little support from volunteers to donations from anybody who has the means to do so, and would be greatly appreciated regardless of where you happen to be.