I thinks so. I also think it's a fair question to ask if social conservtivism automatically implies political conservativism. Is it possible to be a social conservative, but a political liberal - ie to pursue a socially conservative agenda by politically liberal means?
My personal opinion is that people will act responsibly if they understand they'll need to bear the consequences of their actions. The best way to do so is to remove government handouts from the equation. In that respect, less government will encourage more responsibility, and vice versa.