Since Bill Clinton reformed welfare very successfully, we have far less people living on welfare and none making it a career as in the past. Therefore we would not be considered a pure welfare society.
The current number of Americans living below the " official "poverty level is 14.3%. Compared to the wealthy, they are indeed poor. However, their standard of living is equal to or even slightly better than the average European [http://en.wikipedia.org/wiki/Poverty_in_the_United_States ]
Given that 14.3 % live in poverty and 47% pay no federal income tax it looks like we are indeed a welfare state.