I don't think there is a clear cause and effect (or even separation) of those two things. The early views/situations of those who made America are largely the same force which drove the desire for small government and vice versa. I.e. what you believe is ideal in reality is going to be based on the way you weigh things morally just as much as the way you weigh things is going to be based on what ideal is held.

There is, of course, more than one reason people hold the views they do, but I do believe things like rugged individualism & the Protestant work ethic definitely played a major role in why the majority of Americans hold the desires and fears about government they do - particularly in the aspect of these examples. Without those influences, I think what America has tried vs what it has feared would be a very different list today (which is not to say whether it'd've been more successful or not).