Maybe. It depends on what we as a society want our government to spend money on. Considering our current demands in this country (no cuts to entitlements), I think it requires at least that much.
Exhibit A would be the lack of societal collapse during the 90s, when government spending per-capita and as a percentage of GDP was significantly lower than today.
If we're going to cite the 90s, let's not forget that taxes were a good bit higher then as well. In fact, right at the end there, we had a budget surplus.
Yes, and I agree we need to raise taxes (putting me in a very small minority of libertarians). But as to the question of how much government needs to spend in order to have a functioning society, the clear answer is "much less than it spends today".