This is a commonly stated belief, but it's an oversimplification.

Only one in five hundred Americans is a law enforcement officer - https://www.statista.com/statistics/191694/number-of-law-enforcement-officers-in-the-us/

There just simply aren't enough law enforcement officers for them to rule by violence if even 10% of Americans actively opposed them - that's 700,000 law enforcement officers against 33,000,000 Americans.

The law depends on the fact that most citizens, most of the time, actively want to cooperate with the law. And yes, fear of getting caught which means having violence inflicted upon you is certainly a big part of that.

(I'm paraphrasing a little material from near the end of Illuminatus!, which is required reading for anyone today.)