Fascism is a governmental system led by a dictator having complete power, forcibly suppressing opposition and criticism, regimenting all industry, commerce, etc., and emphasizing an aggressive nationalism and often racism. 
It’s pretty common in American politics to imply that those on the American right are fascists. And it’s wrong and based on a false premise and a mis-understanding of the differences between the European right/left and the American right/left.
The problem is that we are using the same terms (left/right) for two different scales and they need to be disambiguated.
(The American Right are not anarchists. They do believe in government, but only enough to ensure our liberties and no more. And clearly there are Europeans that understand the importance of small government.)
Hitler, the poster child of Fascism, was in fact, a man of the American Left despite the repeated attempts to associate him with the American Right based on the confusion noted above. Hitler viewed the state as supreme and wanted a big government with total control so he could serve as it’s dictator, a view that is anathema to American Right. (Interestingly, despite the name of the Nazi party, Hitler was not a socialist although the party was founded on socialism and elements of the party thought that’s what they were working towards .) The three primary ideologies of Communism, Socialism and Fascism all agree on the need for big government and total control. They differ on structure and their motivations for wanting that control.
This is not to say their aren’t fascists in both parties. Anyone that favors big government falls into one of those three ideologies in varying degrees with varying motivations. And that includes President Obama (D), whose recent statements about dictatorially bypassing Congress using executive orders reveal his fascistic tendencies. As does the bridge scandal  and the apparent controversy over the Sandy funding for Hoboken  involving Governor Christie (R).
The real issue in American politics is: do you favor big government / totalitarianism or small government / liberty?