No, many people think that it is quite American due to favoring small government and capitalism.
Here are the things I've heard described as uncharacteristic of a patriotic American:
1. Drinking tea (except for iced tea).
2. Disliking apple pie.
3. Being a communist.
4. Not being a Protestant Christian.
5. Disliking sports, especially baseball or football.
6. Supporting gun control legislation in any form.
7. Disliking Macaroni and Cheese.
8. Expressing disapproval of military action.
9. Speaking a language other than English.
10. Expressing admiration for any other country.
11. Preferring the Metric system.
12. Disliking Country Western music.
13. Burning the American Flag.
But being Libertarian? Never heard that one.
Considering the intelligence of the people who think in such terms, though, I don't regard that perspective as valuable.
EDIT: Please note that I dislike Macaroni and Cheese.