Yeager,
Based on my experience in this area, I have one quick piece of advice: Get a lawyer.
We make lots of jokes about them, but the insurance company employs lots of them and will try to screw you over any way it can (in my case they started off by trying to convince me the accident was my fault when it was absolutely obvious that it was their client's fault).
Get a lawyer.
As to the time, it took about ten days before there was any real progress. They didn't even reliably accept my calls until I had a lawyer.
The lawyer cost me 0% of the amount of money from the vehicle's value settlement and 33% of the pain and suffering settlement. She charged no money up front. She was able to get quick responses from them in my favor where I had only gotten denials and stonewalling. There was no lawsuit filed, just the having somebody who knows the system working for you does wonders. The lawyer I had was a completely positive experience and I have nothing negative to say about the job she did for me. Without her working for me I likely wouldn't have recieved any compensation for my lost wages or pain and suffering.
Based on my experience I must absolutely disagree with AKDejaVu that insurance companies are reasonable and will arrive at fair settlements. The insurance company I was dealing with (not mine, the other guy's) tried to screw me over every time I talked to them, and did some BS game crap as well. They called my grandma (who's credit card my rental was based on) on the Friday of the first weekend I'd had off in four months and told her they weren't going to pay for the rental and to take it back. My grandma got flustered and we took the rental back. I called my lawyer about it Monday morning and she told me to immediately go get another rental. She then called the insurance company to roast them for this. She said that the insurance company pulling that on late Friday afternoon was typical and designed to fluster the claimant. Late Friday afternoon means the claimant often can't reach their lawyer.