Well now, are we talking about what kind of government the Constitution established or what kind of regime is in power at this particular moment? The short answer to the first question is a constitution-based federal republic with strong a democratic tradition (that's what the world factbook says, anyway). But even that isn't sufficient as people can't always agree whether we're a federal union of states or a single nation. If people cannot agree on what the United States should be then what's our basis for comparison in deciding what the United States has become?
Vern, you're an ambitious one, asking such questions on this forum.
