Now this is just a pure assumption, by my guess is that if the fee is bigger than $100, it's probably negotiable.
Whether it is negotiable varies from state to state, regardless of the amount. In your state it is capped at $150 now and by law it must be negotiable but in practice it isn't:
http://www.atg.wa.gov/dealer-advertising
In California, for example, it's capped at $80 but if the dealer chooses to charge a "doc fee," he must charge the same amount to every customer (cash, finance or lease) because that language is spelled out in the statute and class action lawsuits have forced certain dealers to refund the entire amount of the "doc fee" to every customer who was ever charged one since the statute was enacted once it was discovered that the dealer sold one or two cars for cash without charging a "doc fee."
About a dozen states regulate it and in most of those states it is capped at a certain amount -- sometimes under $100, sometimes over, and in states like that all of the dealers in the state end up charging the maximum allowed, even if that maximum is $250. In most states it is completely unregulated. In fact, hilariously, in one state the "doc fee" is capped by law at only $27 but the law allows dealers to charge "administrative fees" that are unregulated.
It's a mess and that's because in many ways we're a collection of states when it comes to laws and regulations, especially in the area of motor vehicle legislation and regulation. Our insurance laws vary from state to state and laws governing the sale of motor vehicles, registration requirements, insurance requirements, taxes, etc. are different from one state to the next.
In answer to the OP's situation, the usual "doc fee" in New Jersey is $349, or at least that's what I believe it usually is but your experience may vary since it's not regulated there.
The usual "doc fee" in Georgia is $599-$699 and in Florida it's $699-$899, but that's just for BMW dealers. I have seen Rolls-Royce dealers along the East Coast charging twice that amount as a "doc fee." The only way to deal with that is to just go with the flow and always ask for the total selling price including all dealer-imposed unofficial fees. If a salesperson lies and misrepresents any of those unofficial fees as an official fee, then the entire transaction could be in legal jeopardy, assuming you can prove you were told that. Official fees, such as taxes, license, title and registration fees cannot be overcharged by the dealer. Just remember that even in unregulated states, the salesperson's authority to lower his dealership's standard "doc fee" may be zero. The best you can do is argue with him over the total selling price, including "doc fee."
Just keep in mind that $1,000 over invoice in California means exactly $1,080 over invoice (including "doc fee") but in Florida it means at least $1,699 over invoice, maybe more.
