Here is how the GOP sees a "War on Poverty" working:
Poverty is caused by people not making enough money. People make money by working at jobs. So to alleviate poverty, we give more people more jobs.
But who are the job creators? They are the small and large businesses. So in order to create more jobs, the government's job is to bolster the industries that created them. They can do that by offering incentives and tax breaks to corporations and to provide the rich, who are the owners of the businesses that create jobs, with as many tax loopholes as possible so that they can funnel that money back into their businesses.
In addition, since we know that some people are lazy, in order to provide incentive for everyone to work, the government should limit the social safety net to temporary and minimal distribution of entitlements. This will force those who would tend to live off the government to go looking for meaningful work, which there should be plenty of if we bolster the rich.
But this is what actually happens:
The tax breaks and incentives given to the rich are not invested into hiring new workers. Rather, it is used to increase redundancy. That is, since the wealthy do not need any more money to live, they use the extra money to buy more of what they already have - newer and bigger houses, yachts, and nice vehicles. They also use it to fund the campaigns of the politicians that work to provide them their extra wealth. What money they do put back into their businesses goes to creating menial, low-end jobs or to fund the development of a more efficient means of production which tends to eliminate jobs. The latest mega-recession caused the job creators to seek ways of producing the same products with less labor. That taught them that they no longer need a huge labor force to produce the same output. So investment capital is often used to increase efficiency so that fewer people will be required for the same output. The result is that fewer people have jobs.
Increasing efficiency is fine, but at some point it doesn't make much sense to produce a lot of product at low cost if there is nobody out there to buy it. Poor people can only buy things that keep them alive another day; they don't worry about gadgets, gizmos, or fancy vacation packages. At some point, employers will have to use their new-found efficiency to produce real, high-paying jobs.
As for the lazy welfare bums the GOP wants to eliminate by starving them back to work, that's a fallacy. Just because someone is out of work does not mean they are lazy or that they would rather not work. To be sure, those people do exist, but they are the exception, not the rule. When the government props up the unemployed, when it pays people entitlements to keep them out of poverty, it creates consumers where before existed only destitute masses. This, in turn, props up the businesses selling the products and services and they will then have the resources to create even more jobs.
History has shown time and again the supply side economics, what George H. W. Bush once called "voodoo economics" is a fallacy. It does not work.