Did you miss the
States part of "United States of America"? Ever since Madison's brilliant compromise at the founding of our current government
http://en.wikipedia.org/wiki/Connecticut_Compromise the USA has tried to be mindful of the sovereignty of the states. (America's previous government, under the Articles of Confederation, was a loose agreement among the states
http://en.wikipedia.org/wiki/State%27s_rights#Controversy_to...) The balance got out of hand in the mid-1800's and a civil war broke out over the issues of states' rights vs. the federal government. Generally, states have the freedom to run elections in any way they want without interference from the federal government.
In fact there was a case in my home state of New Hampshire a few years ago, where a state worker was investigated for not using funds that had been made available by the federal government for each state to use for elections. The state worker's defense was that the money had strings attached; basically there were some restrictions on how the federal money could be used during the election. The investigation was dropped immediately, in favor of the worker. Basically my state would rather spend millions of extra dollars to run the elections than allow the federal government to put restrictions on the way they run elections.