Well... the next question comes into play... how many problems are actually caused by a lack of government involvement, and how many would be fixed by government involvement, and how many actually need fixing?
Just because we have the lowest taxes in the industrialized world does not mean they are not too high, merely that the taxes in other countries are even more out of line.
Crime for one I don't believe is caused by a lack of government spending and I don't think more government spending will solve it. Our culture needs to develop responsibility and real consequences to curb crime.
Poverty. While a shame, our capitalist economy provides the opportunities that enable people to lift themselves out of poverty without government paying them all the time. In fact, the system of programs we have creates a disincentive to work and to excel. Our "poor" are rich beyond the imaginings of many people. What is considered "necessity" has been completely blown out of whack.
Wealth distribution. The problem with the pundits concerned about the distribution of wealth is that they believe wealth is limited. Just because one person has more does not mean that others have less. That's the beauty of our system. There is always room at the table of opportunity for more.