Personally, I do not believe that the United States did have any such obligation. Furthermore, I do not believe that the US intervened in the war for moral or humanitarian reasons.
In my view, the United States entered the war more for economic reasons than for moral or humanitarian reasons. Even before the war, the US did much more business with the Allies than with the Central Powers. After the war began and Britain (illegally) blockaded Germany, this disparity in trade became even greater. The US actually had an economic stake in helping the Allies win the war. I would argue that this economic stake (along with things like political and historical ties) made the US enter the war.
In addition, it is hard to believe that the US actually entered the war to make the world safe for democracy. This was not a war that was based on political ideology. The French and English were democratic, it is true. However, the Russians were on the Allied side and were one of the least democratic countries in Europe until the Tsar was overthrown in 1917. In fact, Russia was probably more of an autocratic state than Germany before the Tsar left power. The Italians also had a monarchy, though their king was not as powerful as the Russian tsar. In short, this was not a Cold War style struggle between democracy and autocracy.
Even if we assume that the US did enter the war to fight for democracy, I still do not think that we had an obligation to do so. The US does not have infinite resources. It is also not capable (as we have seen to our sorrow) of fixing the world’s problems. We have no obligation to spend lives and wealth in a vain attempt to make the world a better place. It may be that we have an obligation to intervene when we see a clear case of moral or humanitarian outrage that it is within our power to solve. However, WWI was not such a situation. I would argue that we had no obligation to enter that war.