most definitely not the nature of their relationship with the US. Many are of no interest to the US and the US needs not apply any pressure on them. A banana republic has to do with the government that runs it, usually corrupt, of no use to its people, eschews law and order and is considered untrustworthy by the outside world. If Israel is a banana republic, don't blame obama' ,look for culprits much closer.
U.S. confirms ISIS computer expert killed in air strike (Reuters)
from the article: Is Israel becoming a banana republic?