We tried that during the industrial revolution. Didn't quite work out that way…
When people are out of work or large classes of people are struggling to get by, it's because we haven't provided a suitable environment in which people can thrive (and yes, most people can and will thrive through their own action in a healthy environment), not because the government has somehow failed to give people enough prosperity.
If it were a traditional business (without the ability to print money or use military force), the U.S. government would frankly be one of the most disastrous companies ever imagined - not just bankrupt (many times over), but mismanaged, fraudulent, and corrupt. A huge portion of our paychecks go to support this company today. And we want more of it?
If we failed anything with small government as you say, those things were growing pains that we would have experienced with a government of any scale. I guess what I'm saying is that it's unfair to blame "small government" for the problems exposed during the industrial revolution.
But I think we both agree that few people still believe that anymore, and that's what worries me most about our country.
From my perspective, the problem is a manifestation of a shift in popular ideals and a growing sense of entitlement.