As of 2005, 12.7% of the US population was below the poverty line. The official poverty line, I believe, is calculated as three times the cost of the "economy food plan" defined by Department of Agriculture (this is because households spend 1/3 of their income on food. If they cannot even afford cheap food, then they are probably impoverished).
That's a sizable number, but it gets even worse if you look at certain minority groups (African-Americans and Lations) and Americans under the age of 18(14.8%, or so Wikipedia tells me).
This statistic is a bit misleading, however. Most people that are "poor" at any given time will not stay there for very long; much like unemployment, poverty tends to be a temporary set-back. Of households that tend to be poor for extended periods of time, roughly half are households headed by a single mother with very little education (IE, high school or below). And a big cause of poverty in individuals is untreated mental instability. It's a bit tough to land a job when the voices in your head are telling you to go kill birds, after all.
So, it's reasonably safe to conclude that being poor and STAYING poor in America is a very, very unusual occurrence for people who have otherwise planned their lives well.
But, there are other questions about poverty that are relevant. For instance, is poverty a cycle? Some liberals and conservatives think so, but disagree on the exact causes. Liberals look at economics: children that are poor have poor life prospects as they are less likely to get a good education and have few connections through their parents.
Conservatives look at psychological and social factors. Children model their parent's unproductive behaviors, making them lazy and unproductive. They also learn how to live a life without working very hard by exploiting welfare, stealing, etc. Hence, children will remain poor.
If anything, I tend to fall more on the conservative spectrum when it comes to the question about the cycle of poverty. Finances are indeed a major issue for many families (college is really goddam expensive these days). However, most of the basic life needs are met by the government for every family. Basic healthcare and immunizations are free or close-to-free, public schools in the US are relatively decent (relative to the rest of the world...not so much compared to the rest of the Western world, perhaps), and the government provides a myriad of various services for the poor, ranging from Headstart to Federal Work Study to student lunches. Considering how tough it is to remain poor in America, financial stress when young should not be a serious issue.
Psychological and social issues? Much more relevant. It's hard to be emotionally stable when you are abused at home. It's hard to know how to act in society when your mother is work at all day and your father bailed out when you were a child. And it's tough to study when your neighborhood is full of drug dealers shooting each other.
So, if I were to launch a new "War on Poverty," I'd be focused on social and psychological issues, and perhaps to get rid of abstinence-only education.
That's my view-point.