"Widowed by age 30, she raised my father and uncle in a tight apartment above a tiny grocery store that she and my grandfather had opened. She worked day and night and sacrificed tremendously to secure a better future for her sons. And sure enough, this young woman – who had the courage to journey to a distant land with hope as her only possession – lifted herself into the ranks of the middle class. Through hard work, her faith and thrift, she was even able to send her two sons to college."
I assume that by referring to his poor grandmother, Cantor was attempting to overturn what he likely considers the myth of means. That is, that one does not need means to become successful - that poverty is no excuse. Yet this is a misunderstanding of socio-economics. It isn't necessarily the fact that someone is poor that makes success difficult. It is what is so highly correlated with poverty - things like single-parenthood, lack of education, lack of parenting skills, lack of cultural knowledge, etc. Cantor's grandmother no doubt possessed many forms of social capital that she was able to leverage into social capital for her family.
In this sense, she would have been financially, but not socially impoverished. The former is a hardship, but no where near as devastating as the latter. Without knowledge, one is indeed powerless. What Cantor assumes in his grandmother, he assumes away in what he would no doubt consider the "undeserving" poor: he assumes she made her own social knowledge, as he assumes others can make their own. Yet this type of knowledge is not self-made. It comes from generations before you, and generations before them. In America we have poverty - social poverty - that goes back generations. Despite whatever convenient faith Cantor and other conservatives claim to have in the individual, their faith cannot overcome the reality of finding oneself without the knowledge and power to be successful.