Does either the civil war in Syria or Iran’s development of nuclear weapons threaten America’s direct national interests, or are America’s interests indirect, at best?
Iran's development of nuclear weapons (assuming that it is happening) threaten America's national interest much more than any outcome to the civil war in Syria. The reason for this is Iran's position on the Persian Gulf. So much of the world's oil goes out of the Persian Gulf through the Strait of Hormuz that the world would be thrown into economic chaos if Iran were able to block the strait. In addition, if Iran were able to use its nuclear power to dominate Iraq, Kuwait, and even Saudi Arabia, it might be able to use its control of their oil to harm the United States.
It is in the national interest of the US to prevent Iran from having this kind of power over such a great proportion of world oil supplies.