The distinction between positive and negative liberties is, indeed, a rather blurry one, but there is generally a difference in mindset between the two. That being said, libertarianism seeks to minimize the size and influence of the government, but they don't seek to abolish it — those that seek to abolish it are anarchists (I'm not sure if I am reading your comment correctly, but it seems that you are advocating for anarchism rather than libertarianism when you said "freedom from a governing authority"). It's important to note that negative liberty is a concept that distinguishes a certain class of liberties — it doesn't require the presence of a government.