To be POTUS, one only needs to win a majority in the Electoral College. Arizona is not a crucial state in presidential elections because it does not have many electoral votes. To be the POTUS there are really about 15 states that you need to win by a majority vote. Those states have enough electoral votes to put any candidate over the top. States like California, Texas, New York, and Florida are the gold standard for most presidential elections.
http://en.wikipedia.org/wiki/Elector...(United_States)