Recently the French have voted down the European constitution. This is a good thing. As it stands the current "European" politicians they have are so caught up in their own bureaucracy that they really don't get anything useful done. An anecdotal example of what they have done: they outlawed selling live animals inside, destroying a generations old tradition at my cousin's home town weekly market. Why approve a hugely bureaucratic constitution so that they can do even more harm?
But that is a problem with the excecution, the real problem lays at the root concept. I believe that a key part of Europe's effectiveness is its diversity and fragmentation. A free trade agreement (EU)? fine. A military alliance (NATO)? good. These keep things stable and prosperous, much like ensuring that companies compete on a fair playing field, but anything beyond this would probably only dull Europe's sharp edge. Seeing the current Italian & German predicaments, perhaps even a monetary union was going too far.
This has an important lesson for the US. Much like Europe attains its overall power from its fragmentation, or atleast used to attain it, the state system within the US also grants us a measure of dynamism within government policy. To pose an analogy: businesses compete through capitalism to attain the best economy, states compete through legislation to attain the best policy. Thus I would propose that some of those problems that we all know are problems, for instance healthcare, we leave to the states to solve. After one has come up with a suitable solution, the federal government can then adapt it, or perhaps just leave it to the states, depending on the solution. If a state screws up, no big deal, someone else can save them. If the Federal government screws up, we're screwed.