In this day and age, the entire would is interconnected. What happens in China affects what happens in Brazil. How the Greek government reacts to their financial problems will naturally affect the Eurozone and then the American economy. Bad or good, the new Greek government will make decisions about their austerity plans and contracts, and that will eventually affect everyone else.
I am not sure how much trading is affected by the United States and Greek actually takes place, but in the world today it seems like everything that takes place has at the very least small ripple effects that touch every country that is modern and connected to the rest of the world.
In as much as we now live in a globalized economic world, political changes on one side of the globe tend to have repercussions in distant places. This is certainly true for Greece and the US, given both the economic integration of the US and Europe, and the consequences for the European Union of Greek political decisions.
Greece had a big effect on the United States, Western Europe, and the entire world in the mid-200s, with their economic crisis. They are also close to Russia, and there are problems with Russia and the Ukraine right now. Thus, I think the stock market will react, and it has really gone down today, in light of Greece's anti-austerity elections.