How long can an insurance co take to pay for your totaled car?

The general answer, absent a contractual or statutory requirement is, "a reasonable time".

When a car is determined to be a total loss, it essentially means that the insurer has decided that the cost of repair exceeds (usually, some statutory) percentage of the actual cash value of the car. In that instance, the law requires that the be declared to be a total loss. The time consuming part of that process can be in determining the actual cash value of a car of like kind, quality, and other features. While there are commercial guides to help in that determination, often there is a period of negotiation with the owner as to the final value.

Many States provide that once a claim has been resolved by agreement as to the value, and all necessary documents have been signed (in this case, proof of claim, title certificate, and other documents that the State or the insurance company may reasonable require), payment must be made within 30 days. However, the period may be shorter or longer and State law will govern.