Considering that the biggest threat to independence is probably the USA themselves… I'm guessing not very far. You'll probably be okay if you cater to businesses and foreign investments, but if you stray too far from the USA's preferred economic model you may suddenly find yourself subject to astroturfed protests, coup attempts, or even straight up military intervention.
Chile's attempt at lukewarm socialism didn't fail from internal causes. Cuba didn't brought embargo on themselves. To name but two. Considering the USA has been at war for almost the entirety of it's history, there must be a couple more.
"Club" was a tame euphemism I only took from the comment I was replying to. I think "Mafia" would be more appropriate.