That is a question for the courts. Amazon obviously fears that Illinois is correct, and the courts will agree with them, or else it wouldn’t threaten it’s business partners.
The courts already decided this once regarding mail order catalogs, the states lost; a nexus has to be physical, a store or warehouse, not a catalog sent through the mail.
The internet is a new form of “mail” order and Illinois is trying to claim that its residents use of Amazon affiliate sales via blog ads constitutes a valid nexus is utter crap.
In the mean time, Amazon is putting pressure on legislatures and governors via their voters, by dumping them from their affiliates program. It’s a smart move.