Poverty is a relative term. If we decided communism was good and split everything up completely evenly among everyone, someone would drop a single penny, and another person would find it. The first person would be in poverty then, and the second person would now be rich.
Compared to the rest of the world, America is rich. Even the poorest people in America are so lucky compared to the poorest of a third-world country.
The person saying "no" seems to think the was on poverty is all over the world. Not saying you're wrong; by that definition, you're right. In America, though, the war on poverty is as won as it will ever be.
Time doesn't change anything - it is our actions. Poverty has not been abolished, yes it has been helped, but we haven't fully gotten rid of it anywhere in the world. When we achieve this (complete abolishment of poverty), then we can declare victory. We will continue to fight poverty, until something major is done. There are so many positive organisations out there making a huge difference, but we haven't won, nor are we close. There are still millions of starving people out there, millions without homes or clothes, that struggle for survival every single day.