Here's an important point/question that I haven't seen raised here.
Why should the United States get involved in conflicts around the world, especially ones wherethe conflicts are rooted in internal strife? Would we appreciate it if there was an internal conflict here, and France, Russia, the UK, or others decided to "intervene" on the behalf of one side or the other?
How is it the duty of the United States to force our will on another sovereign nation? I gave a list of countries ruled by either a single party, monarchy, theocracy, or dictatorship. Should we involve ourselves in their business and tell them how they should run their countries? We can't force democracy on countries just because we happen to think it would be better for them. It has to be something that they do on their own, not something that is decided for them by outside forces.
If people are unhappy enough with the way things are being run in their country, there is a good chance that they will revolt on their own, without anyone else's help. That's how the United States was formed for crying out loud. Our founding fathers had such an issue with how they were being ruled by England that they rose up and declared themselves to be a sovereign nation. Yes, I do realize that we had assistance from the French in a few different ways, but the fact of the matter remains that it was a decision that was made by the majority of American colonists, not something that France, Spain, or Portugal decided for us.
So in answer to the original question. No, the United States is not shirking its duty to democracy. In fact, I challenge the premise of the question at its roots. What duty does the United States have to democracy? I say none. The United States isn't even a democracy by definition. The United States is a Federal Presidential Constitutional Republic that utilizes a representative democracy as part of its checks and balances. So no, the United States is not a democracy, and those that t think otherwise are either ignorant, woefully uninformed, or both.
The United States has a duty to its citizens first and foremost. It does not have a duty to the rest of the world, especially if it comes at the expense of its own citizens.
Nowhere in there do I see anything about imposing democracy on the rest of the world. Nowhere. If you can find it, please let me know because I'm obviously missing something.